Was wondering the differences between Red and Purple quests since Yarpen can choose either.
So I gathered some data. I worked on the side quests part.

First, there're the pie charts. They show the proportion of each type of side quests in all cards. That's more or less (not exactly true, since there can be two side quests of the same type on one card) what you're likely to get with each quest card draw.
If we compare red and purple, first we can see that red has a 12% of monster side quests. Obviously, red focuses more on combat, whereas purple focuses more on travel (+7%) and on gold (+3%).
Then, there's a shift too in the color. Red will give you more purple (+4%) side quests (those that are also used on 16 VP quests) and less red and blue side quests (-3% each).
So what to conclude? There's actually a very slight margin in the total leads side quests given (2%). The main difference is the focus on combat/travel.
But it's not enough to judge. We need to know what are the amounts of leads asked.

For that, there're the bar charts. The amount/card is the mean amount taking into account all 16 quest cards. So it's just the total leads asked divided by 16. There's a total bar but it's not very fair because it weighs gold the same way it does leads and the rate is not exactly 1:1.
Despite that, the main difference again comes from the nature of each color. Purple will ask more gold in average than red (1.13 vs. 0.75). In a 3 quests game, it's roughly a 1.2 difference. Not much, I agree!
The average lead amount is almost similar.
More interesting is the average amount asked, when the specific lead is asked. Red quests almost always ask 3 leads for each color. Now, the rate for 3 leads side quests (4/3) is less good than the one for 2 leads side quests (3/2). And purple quests are in average closer to that 2 than red, if we exclude gold, except for purple leads. As an aside, I think it's a good thing because I find purple leads extremely easy to gather for Dandelion.
Conclusion? Again, not major differences. So, what other criteria to use?

Well, there'a a last chart that shows the average amount of leads asked by each quest. There it's pretty obvious that purple quests will ask more purple leads, some gold (the one 13 gold quest) and red quests more red leads.
So, in that matter the choice mainly depends on your investigation preference. What color do you prefer investigating?

Finally, there's another consideration: the quest rewards. Red will give you a bit more fortune cards in average, but less development (0.13 each). Purple will additionaly grant investigation cards, especially purple ones (0.25). Now, the main difference is that red will create more monsters in average.
Also, keep in mind that almost all red quests (3/4) will trigger combat when completed. All in all, you'll fight a lot more with red, which means you'll need to use your weapons more, thus spend more turns using command.

I say it's pretty balanced and there's no real bad choice. I'd have to compare purple and red investigation cards to be set on that matter.

Yes, I'm answering to my own post but I may need additional space since I intend to give you more analysis and pictures. So, to begin with, a table of what and how many of each dice type you're likely to get with each complete battle roll.

Legend:
Sw = Sword; Sh = Shield; Blk = Blank; Sign = Witcher Sign; Dod = Dodge (Shielded Arrow); Rit = Ritual; Swx2 = Double Sword; SwShx2 = Sword and Double Shield; DodSh = Dodge and Shield; Shx2 = Double Shield
I'll add a few commentaries tomorrow!

Edit: there was a small mistake in the dice roll numbers. It's now fixed! I also added Geralt chances for each of his own hero dices. Will help you if you are forced not to roll one.

So, what does it all mean?
Each number actually represents the amount of the specific die you are likely to get with each roll. Obviously, there are no 0.33 die, it's either 0 or 1. What it means is that in 100 rolls, you should get 33 of this die.
Now, let's take Geralt and Swords. It's a 2.33. So, you can expect 2 Swords per roll, and an additional one every three rolls. So it helps you figuring out what development cards you could need and if you're likely to beat a specific monster given the odds.

As you know, Geralt has an obvious advantage over other heroes in the sense that he throws two more dices. Another that you many not have seen is that you can expect 1 Witcher Sign per roll, that is you can expect to win every success roll. As a consequence, you should not fear Foul Fate cards or Setbacks that ask you to perform these rolls, since you are likely to win them all.
Each other hero however has a 1/3 chance to fail each roll.

The likelihood to get blank dies is equal between each hero. You should get one every other battle in average.

You haven't received a reply, but know that at least I have enjoyed looking at your data.

Interesting write up. I was gonna make a thread to say something but I'll put it here to +1 this thread you've worked.

This game could have used a mutliplayer resume.

Thanks you guys for your replies! It gives me courage to work more for you :) !
johnnygoging, by resume, do you mean go back in a game from which you disconnected? If so, I completely agree! That would be an amazing feature.
I edited my second post with analysis and expanded tables.

Thanks for this analysis. I'm playing TWAG right now and it's good to know about investigation cards. But all in all this game looks pretty balanced.