Okay, home now. Lets do this!
There are quite a few reasons people might find Cave ports better than the original arcade board.
Music: Ports pretty much always have better music. The format offers higher quality music, and most ports allow you to adjust BGM, effects, and voices separately. The one case I can think of where this isn't true is Donpachi on the Saturn, which has pretty poor audio quality.
Arranged modes: This one is obvious. Ports offer a wider variety of game modes than their arcade counterpart (and Mame) do. These vary pretty widely in quality, but are definitely a huge bonus when done well.
Leaderboards/Replays: This pertains more to the 360 ports, but thats where most of Cave's catalog is anyways. The ability to download any replay on the leaderboards is a pretty big bonus. Of course, you can find replays online, but the leaderboards give you more options, which never hurts.
Practice modes: Ports usually allow a Stage Select, and most (all?) of the 360 ports allow you to start at the beginning, midboss, or boss of any stage, and allow you to tweak things like lives, bombs, combo/hit counter, etc, so that you can practice in ideal situations. Mame offers save states, which is another great way to practice, but since the 360 Cave ports are not supported in Mame and are very inaccurate, the ports are the best way to get good at these games.
Bug fixes: This can be good or bad. Good: There is a bug that crashes a certain version of Ketsui if a coin is inserted during the Demonstration. They fixed this in the port. Bad: Pink Sweets has an infinite lives glitch, and it was removed with no option to add it back in, in the otherwise very accurate MMP/PS port.
Okay, I'll touch on the ps2 ports real quick. I can go into specifics as to the accuracy of each 360 port as well, just let me know, I don't mind. They pretty much go into two groups
Arika ports (DDP DOJ and Espgaluda) - These are very, very good ports. Their accuracy is excellent, and they both offer great arranged modes, superplays on disc (as well as more superplays on a bonus dvd), and 240p output (The only Cave ports to offer this on either the ps2 or 360). The one random thing these ports are lacking is the ability to adjust BGM, effects, and voices separately. Other than that, they are top-notch
Cave ports (Ibara, Mushihimesama) - These are basically the polar opposite. Where DOJ and Galuda could be considered the most accurate Cave ports, these are considered the least accurate. Mushi is missing about half its slowdown, and Ibara is missing practically all slowdown. Both ports also have a forced filter that cannot be turned off (although there is a 240p patch that helps these games to look nicer). The arranged modes are still good though, and these ports actually do offer separate BGM, effects, and voice sliders. It has been proven that very high scores can still be achieved on the ps2 port of Ibara, so I do think it gets more hate than it deserves. People seem to be more bothered by the muddy graphics than the actual game inaccuracies. Plus, its the only Ibara port, and having CD-quality music in this game is great. If you have a j360 (or jtagged), go for the 360 port of Mushi over the ps2 port.
Alright, hope that helped.
Hopefully I didn't miss too much! Oh, and in case it wasn't obvious, I definitely prefer ports over the real deal. I would never dream of trying to learn Dodonpachi chaining on the actual PCB. I do really enjoy any opportunity I have to play the original boards though.
