Turn-based combat allows for more tactics that involve more than "Rush at the enemy, frantically clicking every button".
I played both the IE games and Fallouts and I still cannot be arsed to finish any of the IE games (except Planescape because it deserved to be finished) while I finished both the Fallouts. Give me turn-based combat or give me death...after I spend my Action Points :D.

I don't understand. Why would you have to "Rush at the enemy, frantically clicking every button"? You know you can pause at any time right?
Tactically, I don't see how you can argue that fallout gives more options than IE games. BG gives you 6 characters of vastly different classes which you can directly control and adjust their inventeories.
What can you tactically do in fallout that you cannot do in IE games?

You can aim at specific body parts. You can use area of effect weaponry (grenades, rocket launchers...the fireballs of Fallout I suppose) without worrying about splash damage as you would in the IE games.

Aiming at body parts is a cool feature. But that one ability in fallout combat is matched by tons of abilities in BG (including the archer's called shot) which vary by class, giving more tactical options.
The splash damage in BG requires you to be MORE tactical.
I honestly do not see how you can argue that fallout combat "allows for more tactics" when you consider that you control 6 characters in BG, vastly different classes, melee, ranged, and magic combat, plus all the buffs, potions, and many more equipment options.
The PC in BG undeniably has more options in combat than the vault dweller, plus you have 5 more party members which you actually control.
So I ask again, what is the advantage of turn based combat?

First off, stick with it, it's well worth getting to the end of the games, both 1 and 2. Even if you cannot stand the combat.
I've never played Baldurs gate of any description so cannot compare, but Fallout was my first turn based combat game and I was very dubious at first.
In fact, first time I picked Fallout up I quit it after 30 minutes because I thought the entire game was turn based (I inadvertantly got into combat with the rats in the vault 13 caves and just kept walking without really knowing what was going on, a good argument to read the manual before you play).
Think of it like a game of chess, the turn based gives you time to plan, consider your moves etc, then it can punish you unequivocally if you make a bad decision..
Do you fire or access inventory and heal? Do you get closer to improve chance to hit, or do you take a long shot and duck back behind cover. The tactics are endless if you put some effort into it.
I quite enjoyed the tension and the satifaction of getting a critical hit and exploding some heads. The random nature of the dice roll means you never quite know how combat will turn out, and it doesn't come down to quick reactions. I can play a first person shooter as well as the next guy but its quite refreshing to have a game where reaction time doesn't come into it.
You can have a super character and an unlucky dice roll and bad decision can bring the whole game to a crushing end, thats the kind of randomness you could expect from an unknown post nuclear wasteland and thats why it works so well.
The random element plays a big part, you make your move and then you can only witness while your NPC's and enemies play out their moves. It can be hugely frustrating and very satisfying at the same time.
I can't see how fallout would work any other way.

It sounds like you have answered your own question. If you cannot see an advantage of turn based combat then there isn't one is there?
I think it comes down to preference. I enjoyed Fallout combat and BG, although for the sequel it took me a while to figure out the spells. There are certainly more tactical options in BG.
But my personal favourite has to be the combat found in TOEE, which is turn-based.
Not because it is turn-based but just because of the amount of combat options and the graphical style.

Problem with Fallout combat isn't turn-based combat (which I find inherendly superior to anyhing real time combat has to offer); it's the lack of proper inventory handling and most of all, lack of ability to control your team mates. I also wish combat was be more tactical like in X-COM or Jagged Alliance (combining FO setting and story, BG2 party interaction, X-COM destructable terrain and JA2 tactical combat would make perfect game) games but even the first two would improve the combat immensely.
In general Turn-Based is best for larger scale tactical battles. The bigger team(s) and battle area, the more advantage it has over real time. Large battles with many people to controll in battlefield streching several screens would be nightmare to handle in real time.
Real time is better for games with lot of smaller (both in terms of combat area and number characters you control - in turn based combat you can easily handle two (or more) characters in separate battles in different sides of huge map, in real time it's near impossible follow both battles) battles where you have small or no party to control. Lot's of small insignificant battles gets boring fast in turn based games while in real time you can quickly bash your way thru them.

Hmmm... On reflection, I don't like the TB combat itself, per se, but I do like how it's one of the few TB combat games out there with guns!
I've played with a lot of TB combat systems, and Fallout's is definitely one of the more interesting ones, especially if you turn the firing and movement speeds up to reduce the time between turns. I still prefer Real-Time w/ Pause systems best for tactical combat, but I've played with systems much more unrewarding and difficult to use than Fallout's.

The combat system in BG2 (where combat plays the main part unlike in FO) is more modern than in Fallout, which is older and was released before the Command&Conquer style point and click was brought into the rpg world.
I played Fallout after playing all the infinity engine games but I liked the combat nevertheless, I liked it even more. Turn based combat felt more strategic, while BG2 battles felt rather like point-click-die, like the Command&Conquer mini battles (which I liked a lot btw). Fallout battles felt more like controlled acting (especially when you aimed at body parts), while battles in IE games felt more like floating through, sometimes unrealistically drawing the time-out card to give commands for doing fantasy stuff.
I liked that NPCs do fight on their own and don't have to be babysitted like in BG2, it's more realistic, doesn't take the personality away from them and speeds up the game.

In my opinion, Fallout's TB combat matched the lone wanderer feel of the game perfectly. I like that you cannot directly control your NPCs, because they are actually different people, they're not your puppets, they've got their own personality and their own agenda. You're even lucky they can be controlled at all, and they don't start randomly attacking people they don't like.
I do think that turn-based combat can offer more tactics than real time systems. I just love that you can take down a slow super mutant with just a pistol without taking a single hit, if you cleverly step out of cover, shoot, and step back before your turn ends. In real time, you would be relying on your AC to avoid the bullets flying from its minigun as soon as you're in its line of sight. While TB is not the most realistic combat system ever, it is certainly the most fun for me.
This doesn't mean it's not annoying a bit when facing dozens of rats at level 50. :)

Well that might work if they actually had even remotely good combat AI. I hardly would call it realistic that they seem to talk pretty intelligently but next moment unleash their minigun on entire party because AI does not seem to realise we are between him and the hostile he is targetting. Unless NPC's can act at least semi intelligently in combat I must rather have full controll over them.

I disagree. I can handle turn based for the small battle, but I find it mind numbing in large battles.
Spoliers, I guess:
In the boneyard battle I found it impossible to lead the blades into combat against the regulators. The turns took forever and I couldn't even see everything that was happening because it was beyond my PC's vision range. Dogmeat and Ian died repeatedly because we spawn inbetween the regulators and the blades. I tried it on my own and while I could have killed everyone I had no interest in spending 30 more minutes waiting, so I just told the blade leader that I didn't want to fight and let them deal with it. LAME.
I do agree, Petrell, that there is nothing realistic about the lack of party control in the game. Maybe if the characters were remotely fleshed out and had decent AI it would be okay. But maybe people who are more imaginative than I can RP a scenario where the PC takes a bunch of mentally disabled survivors under his wing and gives them heavy weapons.

I enjoy turn based games because they allow me to consider possibilities and tactics. That's not to say that I don't enjoy the infinity engine games as well. I'd enjoy some way to take the combat from Fallout Tactics and mod it into Fallouts 1 and 2.
edit: I mean to say the turn based version of Tactics' combat.

Well have you played grand stategy type games or in general stategy games where you have to handle multiple fronts? I have quite few and in my experience turn based is only way to go with this kind of games. You simply can't be in many places at the same time.
As for your Boneyard battle, isn't that a flaw in scenario desing. At very least you should be able to choose where you start in combat. Obiously that would have only limited help with braindead companions rushing into middle of the combat and getting themselves killed. Obviously players vision range should be greater also, at least for this particular battle. Having controll over your party would help alot as you could distribute you party over the battlefield giving clearer view of the situation and allowing you to help where needed.