Fizz's invulnerability is way better than stealth. There are a lot of champions that have that. There is also Fiora, Master Yi, Zed, Kalista(for her ally), and probably more that I'm not sure about or am simply unaware of. I don't think Kayle belongs to this group since I think her ultimate only prevents damage, the affected champion can still be disabled if I am not mistaken.
As for Shaco's third skill, the passive doesn't work while the active is in cooldown, and it's a skill of a Shaco player to use the passive sometimes for a longer duration slow but without damage, or to throw the shivs for the shorter duration slow but burst damage being added to the attack. The choice is not always easy.
Shaco is faced with many choices. When he lays his traps he has to choose where to plant them. He also has to choose whether he wants to plant them in sight of the opponents or not. His traps are capable of tremendous damage, much more than the shivs, but they are also easily countered. They could be destroyed accidentally or on purpose by spells and they can be revealed with a free trinket and attacked at range.
I do like Shaco, but I don't think he's as strong of a champion as many others because his mechanics are not that great compared to other champions. Warwick and Ashe are a couple of classic examples of champions with superior mechanics. Ashe has a third skill's passive that gains her additional gold, and to add on top of that, her basic ability promotes the purchase of the gold income item that gives her increased critical strike chance. Warwick has an ultimate that does way more for lock down than Shaco can do. On top of that, he can generally outrun his opponents if they survive the initial disable. His ultimate isn't a skill shot just as Shaco's third skill isn't.
Shaco is a champion that rewards the player for being creative and tricky. However, I actually feel he's not as great on Summoner's Rift as he could be. I think the main problem is that fights can happen anywhere and you simply can't plant that many traps because the duration does not scale with AP. I made a thread about this, suggesting that every 100 points or so of AP should give +15 seconds duration, but Riot has yet to mention if they think it's a good idea.
counters Shaco now, did you know that? Smite the raptors, walk near any of the wards they probably have around, true vision on Shaco. It actually punishes Shaco for getting deep wards down.
He can never hide from 
. If 
sees him once, Shaco has to turn and run or be revealed for his entire stealth duration.