Going to potentially open up a can of worms
And I have actually ran the game on a laptop I used to have. It would have the occasional stutter problem on a Core i7, 8GB RAM, and a Geforce 750m card which tends to be faster than the very best integrated graphics available.
Feel free to correct me if I'm wrong or discuss this in your own opinion. I don't know everything, especially about game development.
Note: I'm talking about an official version of the game released by the developers, not about emulation.
Feel free to correct me if I'm wrong or discuss this in your own opinion.
I'm not sure what your question or theory is.
Yes, resolution is one of the things that slow down games. I often preferring dropping the resolution (and letting the monitor up-scale it) while cranking up the graphic settings of the computer games I'm playing.
I haven't played the PC's version of Sonic Adventure 2, but I don't think the resolution increase is the cause of the slowdown. Sonic Adventure 2 for the Dreamcast probably used different APIs and 3D graphics libraries and so on. They're probably running the entire game in an emulator/virtual-machine, which would significantly slow everything down. Especially if the emulation is running entirely in software, instead working with the modern videocard.
Many older games are packaged with emulators to run on modern hardware. This is a good solution, commercially, because you invest the effort in writing the emulator for the platform, and then can "port" multiple games very easily using the same emulation layer. Also, who knows where the old source-code and original assets were stored? Maybe they no longer have the sourcecode. But emulation doesn't need the original source code to work.
This is probably what Nintendo does for the Wii/WiiU and 3DS and their 'virtual console' games. This is definitely what LucasArts does for their old Star Wars games (having bought and played Star Wars: Dark Forces via Steam). Many of Good Old Game's releases are running off of emulators (usually DOSBox).
Or perhaps Sonic Adventure 2 runs slowly just because it was really buggy even on the Dreamcast.
Screen resolution is not the only thing that affects the frame rate of a game, and with old games in new hardware it shouldn't be a problem. Probably it's just a matter of making a quick release with not much focus in optimization.
We will never know how much from the original Dreamcast code was reused for the PC port (if it's actually a port and not an emulator running the game like Servant said, which could easily be the case here), but probably they needed to change some things at the core level and that could really affect the performance.
Anyway, it's not that uncommon to found PC games ported from consoles that run worse than you would expect. Look at Dark Souls, the developer even recognized that they just wanted to get it released as soon as possible and the game was released with lots of problems: http://www.pcgamer.com/2013/12/19/dark-souls-producer-admits-pc-port-was-rushed-promises-sequel-will-be-a-good-pc-experience/
Sega's recent rereleases of Dreamcast games are all utter crap without much effort put into them, just saying. They're basically just a rushed port of the original code. (the original ports of Sonic Adventure DX and Sonic Adventure 2 Battle where infinitely better)
Or perhaps Sonic Adventure 2 runs slowly just because it was really buggy even on the Dreamcast.
Pretty sure it was 30FPS there.