I never played the Freespace series but I remember Freelancer as being a very fun game. Can someone give me a honest comparison between both? Also, should I begin with Freespace 1 or can I skip to Freespace 2?

Freelancer and Freespace are all around different styles, referring to the same type of game : space sim.
Freespace is a straight forward shooter, with strong done campaigns and nice concept
Freelancer is more complex type of space sim where the player have the possibility to choose the trade rute and not the fight rute (unless he have to).
Personally, i believe Freespace has more flavor and is more of what a space sim should be.
In the same category as Freespace you can have also Starlancer, Dark Star one, wing commander.
My advice, go for both, as the story line is very nice and you will feel more like part of it.

I'm playing Freelancer at the moment, and it is a different game to Freespace. That might seem quite obvious, but when choosing between them it might be worth asking what you want from your space sim.
Would you like the choice (or, at least apparent choice) of what to do and where to go. Does an open ended universe float your boat? Do you fancy an rpg style game? In a nutshell, that is what Freelancer is offering you. On the other, Freespace doesn't give you these options. You follow a campaign and a story line, it is classically linear. Let's go into a little more detail though.
It's been a while since I played Freespace and Freespace 2. In fact, I only truely remember Freespace 2. But what I remember was a fantastic story, with fantastic missions. A lot of people dislike linear gameplay now days, the gaming community prefers choice. It's a buz word. But, linear games can be fantastic because of the atmosphere, the story you're jumping into. Does the game make you feel part of it? Freespace excels in creating an atmosphere. You feel vunerable, space feels big, capital ships are massive, lasers are bright, explossions are blinding. It truely is a GoG, but the community around it still exists. There are mods to extend gameplay, patches to make it even mor beautiful and this is the funny thing. Freelancer offers an open ended universe, presumably you've got replayability? Not really... I'll touch more on that, but because of the Freespace community, you'll be coming back tsucceedFo Freespace again and again.
Freelancer doesn't do any of this as well. It is a different game, you can trade, take missions where you want and when you want. But only once you done the main mission.. the storyline. I think you can stop the storyline at some point, but why? It's the best mission. It's a challenging mission. The random missions you find everywhere else are a bore. Your character is a bore, and the storyline is really broken by him. Freelancers combat pales in comparison to Freespace... Capital ships seem small.. space seems small... weapons seem small.
I didn't mean to turn this post into a big ranting opinion.. but I just got passionate about Freespace... maybe you can too? ;-)

Actualy, while he should play the campaign of the first game, he doesn't have to play it in the first games (rather ugly) engine. There is a mod that ports the campaign of the first game into the second.
http://fsport.hard-light.net/website/

It's funny that you ask for a comparison because FREElancer is a sequel to STARlancer, though they play much differently, and STARlancer has more in common with FreeSPACE than any game I've seen before. STARlancer has a more conventional control scheme and all of the mercantile elements absent, but those things were what held FREElancer back anyways so STARlancer comes out on top in my mind.
Also, please excuse my shouting for clarity.

Yes, my recollection of Freespace 2 (haven't played it for a while; just bought and downloaded it but not played it yet) is that it is very much a linear storyline, along the same lines as the Wing Commander series, and X-Wing, Tie Fighter etc.
I'd say Freelancer is actually somewhere in the middle compared to what some posts have said. It's kind of open-ended, but not really - it's still largely around just following the main story. You might divert a little bit, but not much. And no joystick play is an interesting choice for a space sim.
The ultimate in open-ended space sims that I've found (although back in the old days it was hard to beat Privateer 1, Righteous Fire and 2) has to be X3. The fact that there is a storyline is almost completely incidental to building your trade and military empire.
Talk about the massive capital ships in Freespace; try owning 10 of them, and calling them all in for a massive clearance of a Xenon sector. Absolutely fantastic.
It was mentioned in an earlier post, but please, for the love of the flying spaghetti monster; do not buy Darkstar One. An absolutely horrendous example of the genre. Drivel.

Is Freespace series anything like the Egosoft's X space-sim series?
(X2, X3: Reunion, the upcoming X3: Terran?)

I think Freelancer is a vaguely similar concept but X is much, much more 'hardcore', I tried X but found it too hard to get into for it to be worth my time :( (and this coming from someone who plays EVE online where after 2 years I still feel like a total noob!).
Freespace however is nothing like X except for the fact they both have joystick control and they are both in space, and you can blow stuff up in both (though the focus of X is mainly on trade and industry, that sort of thing, from what I've seen)

Well, if you want to play a space-sim with open 'world' and countless possibilities, you should try X3 - but you'll need a lot of patience to play that - rather than Freelancer. Freelancer is more... mainstream. And yes, Freespace is something totaly different :D Though Starlancer (as stated before) has pretty much same gameplay as Freespace and it has a nice story, too...

Total apples and oranges. Freelance is a more open-ended game with combat and trading (giggle, yeah, right) elements that's more like an RPG in space. Freespace 1 and 2 are more straight forward, WWII-style space combat sims with a fixed, linear plot. They're both a lot of fun, but Freespace 2 is the shit.
You CAN skip Freespace 1 and go to 2, but you'd miss a lot of the awesome backstory, so I'd say play both in order.

Heh, only get X3 if you want to take a crack at a second job that you really don't get paid for. ;)

Um... Yes, that's kinda truth, it is time consuming :D

So much hate for Darkstar One? It saddens me. Sure the game was utterly broken, but I found myself writing down prices of things at stations to trade. It was VERY far from perfect, and far from great-but weren't some aspects at least fun?
It might be that I picked it up for 10 dollars. That could be it.

FREESPACE- and if you want freelancer then play starlancer!
i like privateer style games but i really prefer militairy space shooters theres something nice about being a part of a squad and having a cap ship to protect.