Just to comment on a few things...
First of all, Civ3's combat system... sucks. Look me straight in the face and tell me that a Tank unit should have ANY chance of defeat at the hands of a musketman (or spearman). Its stupid. Having said that though, it is VERY easy to fix these problems. By making the AD spread much larger and giving additional hitpoints to more technologically advanced units, you can all but elimate the problem.
And please, no posts about "well uh, uh, actually, it is possible, because you know the tank barrells could get clogged and and blow up!" oh cmon... a tank unit, or armored division is not just tanks, it has infantry components, artillery attachments etc.
So does Civ3's combat system suck? yes. Is it easily fixable? yes. For instance, giving a tank in Civ3 a AD or 32,16 instead of 16,8 makes it almost impossible to have it lose to a gunpowder type unit. At the same time using that same 2:1 ration on all modern units will ensure modern combat is not changed.
I won't even mention how stupid Naval Combat is in Civ3...
Barbarians:
I like Civ3 barbarians, and I love the horde idea they came up with. Unfortunately the 'horde' is all but a cakewalk for a couple of units because of the ridicolous bonus a player recieves against barbarians. I can't remember if the bonus is in Civ2 or not... either way, the Civ3 barbarians (w/ some tweaking to their combat effectiveness) can be a very real threat early on, and do a great job of representing their effect on history. Later on, Privateers and their hidden nationality do a great job of representing piracy.
Some may disagree, but I like how you don't lose cities to Barbarians. Too many issues, and losing a lot of gold or having your improvements pillaged etc. is still a pretty good way to represent their effect.
In Civ2, barbarians are random creations w/out any rhyme or reason. Their ability to capture cities made them much more dangerous than in Civ3. However this lead to some exploits and generally dumb circumstances involving them... Also, there were 'modern' guerillas, who had cavalry and artillery. A bit unrealistic? Well depends on your viewpoint, but in an epic game like Civ I think it was.
Cartoonish leaderheads...
They can be a little ridicolous, but at the same time, you could always mod the game with flags of the respected nations. This way you can also have anyone you want to at the helm of the nations.
Finally, corruption (sorry its easy for me to start rambling on something I spend a lot of time on

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Corruption in Civ3 is... about right. Just look at the Roman Empire, heck, look at the United States today. You can't tell me there is no sizable corruption occuring, whether or not we do not know about it. It helps balance gameplay. Large empires experience rampant corruption. WOW, what a ... realistic concept. In Civ2 communism erased corruption altogether, along with Democracy. Fun to have a nice little perfect empire? yes, realistic? heck no.
Are there ways to get around corruption? Of course, police officers, forbidden palace, communism (communal corruption) and more advanced forms of government alleviate but do not eliminate corruption, as it should be.
Well, I could ramble on a lot more, as I've played both games... well, a lot. And I like both games a lot, so sometimes its tough for me to say which is better. Whenever I have trouble deciding, I just remember all the Civ2 AI cheating. "Oh look, that AI bomber has been flying for THREE turns straight and hasn't run out fuel, wish I could do that.."
