Surprised you have to ask. Most of the time the second game in a series is a lot more refined.
My picks:
Assassin's Creed 2
First one was just horrible, the second one's close to perfect in comparison.
Star Wars: Battlefront 2
Don't really like the Battlefront games to begin with, but I'd still say the second one better satisfies peoples' expectations of what the game should've offered. "Hero" characters were an excellent feature, and they all wade into combat pretty nicely.
Mega Man Zero 2, 3, and 4
Better, betterer, betterest. The music just kept getting better, the story got more interesting, and the customization features got a lot stronger from one game to the next.
Devil May Cry 3
Much more refined and much less clumsy than Devil May Cry 1. Dante's Fighting Styles are exactly what the game needed to round him out. The story's a lot more coherent, and the acting--for such an incredibly cheesy game--is a lot stronger and more believable.
Ratchet and Clank: Up Your Arsenal
The perfect R&C game. None before it was half as good, none after it has achieved its greatness. Best variety of weapons, best variety of missions, ranging from war zones to infiltration to good old fashioned exploration.
Kingdom Hearts 2
Oh, I'm sorry! I must be on crack. This game sucked. The first one was way better in every respect. The only thing this game has going for it is Drive forms. Never mind.
Jak II
There'll be more than a few people who disagree with me here, but I'll just come out and say it: Jak and Daxter, the original, sucked. Its world had a lot of classic platformer charm to it, but all in all it was a wholly inferior clone of Banjo Kazooie. Its story was really weak, bordering on lazy, and its levels ranged from "nothing special" to "frustrating" to "THIS IS PAINFUL TO PLAY IT'S SO BAD." It wouldn't be so bad if there were a stronger sense of reward to it, but Jak never obtains new abilities, and new levels never offer anything new or interesting to explore--whereas Mario 64, another game with no abilities or upgrades to unlock, makes up for it by creating a host of unique challenges in each level to give you a fresh way of thinking about the abilities Mario's been carrying with him from the start of the game. Jak? Same 5 or 6 challenges in each level, different layout, some horrible, frustrating new gimmick to piss players off. Piece of shit game.
Jak II, however: the atmosphere and the story are a lot more interesting, sort of reminding me of Final Fantasy 7 or the Lucasarts adventure game Full Throttle. Jak obtains new abilities both in the form of new weapons and new powers for his Dark Jak form, both of which offered Naughty Dog the opportunity to develop more interesting and more challenging enemies to fight. In a way they were kind of jumping on the sandbox game bandwagon by including guns and giving players cars to hijack, but these were each taken with a unique spin, the weapons were legitimately well-designed--and for that matter worked a lot better than guns ever did in any Grand Theft Auto game before it--and the game still felt like it was being true to its platformer roots. Platforming sections were more straightforward, didn't overstay their welcome, and were more memorable, and with the addition of the hoverboard it gave the game a very "complete" feel, like it was really squeezing the lemon for all it was worth when it came to utilizing the futuristic setting for gameplay ideas. Simply put, a much better game. Of course Naughty Dog couldn't make bosses to save their bloody lives and STILL can't, but whatever.
Okay, got a little overly analytical with that one...
Mass Effect 2
Much tighter game than the first in just about every way. Showcased what was unique about the Mass Effect setting a lot more easily and a lot more early on than the first game did; comparatively the first one just felt like a shallow ripoff of--somehow--both Star Trek AND Star Wars, like Bioware was just phoning in Knights of the Old Republic. ME2 changed my mind on that.
Sonic 3 & Knuckles
Much tighter controls than Sonic 1 or 2. As in: actually tolerable to play.
Meh, I'm done now. I'm gonna go get some sleep.