This forum really needs moderation for unnecessary posts.
I pretty much agree with everything Aqo said. osu!mania offers skin customization, smooth multiplayer experience, IRC chat, and spectating other players, all of which are rarely found in other rhythm games. osu!mania is excellent if you're a multiplayer fanatic or a frequent spectator of (higher level) players on YouTube. The lack of ranked osu!mania mapsets often forces players to play auto-converted maps, and I feel that this really hinders VSRG veterans from truly enjoying the game. For now, we can expect an exciting future for osu!mania.
O2Jam is more based on Long Notes (LN) than normal notes. The judgment is based on beats rather than milliseconds (If you hit A key when it was B beats off at C BPM, you get D judgment). The overall judgment is easy compared to other games; roughly speaking, a 300g, 300, or 200 in osu!mania is equivalent to a COOL in O2Jam. Players mainly choose O2Jam for LN practice, but ever since the official servers went down, it's hard to find a good server to play on.
LR2 has no mercy. It throws you into the fray without any tutorials. At the same time, LR2 offers many features that help you improve. You can find a rival system (where the system compares your scores on a particular map with your rivals, and determines who "wins". Meant to serve as motivation to beat your rival's score, subtly improving your skills), tiered courses (LR2 has no actual rankings. Players are classified according to the most difficult four-map course they can play), and an in-game target/goal setting. LR2 is great for players who couldn't care less about silly numbers and ranks, and want to focus solely on getting better at the game. However, some of LR2's major drawbacks include the website being written entirely in Japanese, and the client having many bugs (crashing after a couple of maps, for instance).
IIDX should only be considered if you can find a cabinet nearby. I have never tried IIDX yet, so I can't really comment on its advantages, but I can already think of one possible drawback: It's an arcade game. Money, transit, time...