There are several games that have the original game and the sequel both on DC. Sometimes the sequel is a clear improvement in many areas, but other time the sequel maybe isn't up to snuff or as cool as the original game was, and the original game stands up better to the test of time. Here is a short list I just thought of - which do you like better and why?

*Evolution & Evolution 2 (never played Evo 1 so no comment)
*Aerowings 1 & Aerowings 2 (never played Aero 1 so no comment)
*Tokyo Xtreme Racer 1 & TXR2 (TXR2 is a clear improvement imo, many more cars, highway and better graphcis)
*Powerstone 1 & Powerstone 2 (Powerstone 2 is my fav, 4 player mode is a blast and the new items and stages are impressive, #1 is still a good game though I don't play it anymore)
*Marvel vs Capcom & MVC2 (I like MVC2 because it has maybe 4x the characters ;) Definitely like the music more in MVC1 though)
*Capcom vs SNK 1 & CVS2 (I like CVS1 because I am a fan of 4 button SNK/KOF style fighting games, and CVS1 plays more like one, I also like the music a lot more and music is an important factor for me)
*Crazy Taxi 1 & Crazy Taxi 2 (I know CT1 is a sacred and classic game, but I actually really like the hop ability in 2. These days I think I would enjoy 2 a lot more often than 1)
*Gigawing & Gigawing 2 (I've been playing Gigawing 2 A LOT recently and I think I'm getting tired of it. I think gigawing 1 plays faster, has cool music, and potentially cooler characters. The 2d graphics are a little more timeless than the good-for-DC yet dated looking 3D graphics of Gigawing 2. GW2 is still a really good game though)
*KOF99DM, 99Evo, 2000, 2001, 2002 (I haven't played all of these on DC so I'll defer this)
*Sonic Adventure 1 & Sonic Adventure 2 (These are fairly different games actually imo, but SA2 was definitely tighter in the controls with better graphics, my vote is for SA2 though I miss the more open world feel of SA1)

That's all I can think of for now. I bet there are some more, especially if you are counting JPN RPGs or date sims, which you shouldn't ;)