Open PS2 Loader is actively developed and as i heard it plays some games now that HD Loader did not*. It can't install games itself yet, you have to use HD Loader or a PC for that, but you don't need to patch any games. Open PS2 Loader contains some patches for some games already and there are more compatiblity modes to get them to work than in HD Loader if a game won't work. It also allows you to surpass online game protection, if you read the corret game id with your retail disc. Oh and it's compatible with most modchips now, but i don't see the point in a modchip when having a network adapter.
*I can't tell you which ones in specific, as all my games either work in both, or they don't work in both
PS: To me it looks like Open PS2 Loader development concentrates on HDD and network loading, USB loading just benefits from general improvements