There has to be latency issues, but as anyone that used to play Quake over dial-up can tell you: you get used to it.
A local client does not suffer from input latency and the client does not validate camera movement (mouselook) to server snapshots . There's also some leeway into other kinds of movement so latency jitter and a few dropped packets do not inadvertently disrupt the player's flow. Furthermore, the server does latency compensation that is crucial for actually hitting anything, especially with hitscan weapons lacking AoE damage. All the above is a very simplified explanation of what happens, more details at following PDF [1].
Games on OnLive lack the above features and you also have input lag, where, for example, a camera movement with the mouse will take the full network RTT plus processing time to reflect on the client's screen.
[1] http://web.cs.wpi.edu/~claypool/courses/4513-B03/papers/game...
That's true, I remember there being lots of prediction and compensation in QuakeWorld especially.
I haven't played the OnLive stuff so I'm not sure what it's like, but with a decent connection I'm guessing it's something that your brain just ends up dealing with. Although if it's anything like using RDC for a long period of time I can see it getting annoying.
I've spent several playing first person shooters and it's easy to forget you're not playing locally.