Ginobili came into the league quite old (age 25) with loads of international experience, and he did show flashes of passing ability in EuroLeagues that were harsh in crediting players with assists. Most significantly, he could really get to the line even back then, a credit to his ballhandling ability and his nose for slashing. You're right about the three point shooting--he really developed great consistency with it in the NBA, but it helped that he took over a third of his shots as threes during his last three years in Europe, helping him gain more ease with the transition.
Casspi's still very young (21), and obviously we'll get a better read when we see the actual games, but right now I see him more as a hustle player. I'd like to fantasize about 6'8" SG/SF with PG abilities because it sounds innately more appealing than a 6'8" SF/PF, but he's sort of lacking in those three markers Ginobili had. He's really poor in passing the ball (even if it's a product of the team dynamic, it's still very poor), and while he did show he could shoot threes he only took 1/5th of his shots from there, so the transition might be less easier, and he's only shown ordinary ability to get to the line--he doesn't seem to possess great ballhandling skills.
Passing, ballhandling, and shooting from long range are three major elements of guards, and right now he seems mediocre to poor in them--granted he's only 21 and he's had Turk comparisons bandied about him, and if developed properly he could be primed for a huge upswing, but based on what I'm seeing right now it's very Harpring/Nocioni-esque.
P.S. The team construct will also come into play--when Ginobili came into the league he played quite a bit backing up only Stephen Jackson; Jackson left the following year and he basically got his chance to shine afterwards. Omri has to fight Jason Thompson, Sean May and Donte Greene at PF and Andres Nocioni and Francisco Garcia at SG. By midseason however there could be a chance to get minutes--if Noc gets traded or if Sean May gets injured/Donte doesn't produce, then he will really get more of a chance. Of course many variables will come into play there, but we'll see.