I've played every class up through level 6, and up to that point (which is admittedly very low) I stand by my statements. Stalkers are the most difficult solo class in the game, with the possibly exception of Corruptors. What I have seen on the forums would seem to back this up (though the higher you get, the harder it is to solo a Dominator). I'm glad that you're having success with yours, and I never said that such success wasn't possible, but compare it to a Brute or a Mastermind and I think you'll find that the Stalker is, while still viable, more difficult to solo.
As for PvP, what I have heard from dozens of people is that Hide is way too easy to see through. While other characters are running around fighting and blasting and waging war, Stalkers are forced to hide, choose their targets, and then run as soon as they've dropped one guy. On the one hand I think this is great, because that's exactly what an assassin is supposed to do, and I'm glad they were able to balance the game in such a way that it encourages this type of thematic play. On the other hand, this play style is incredibly slow, and Stalker are usually only able to rack up a fraction of the PvP kills of any other class. If that doesn't bother you, great, but I know it does bother a lot of people.
The strength of a Stalker in PvP is that they can one-shot almost anything of appropriate level, which is why people are constantly clamoring for a Stalker nerf. I hope that they don't nerf the, because that would seem to lead Stalkers more toward the role of a WoW rogue: an agile, fragile warrior that deals a ton of damage in a long fight. I like the concept of the CoV Stalker much, much better: the hidden assassin who slips in, nails somebody, and slips out again unseen. It's kind of unfair for the squishy classes who get one-shotted, but proper back up and anti-Hide preparation is apparently easy enough to pull off that the only ones a Stalker can really one-shot are the ones who make stupid mistakes.
While I'm discussing strengths, I should point out that Stalker do have one very impressive solo advantage: they can zoom through boss-kill missions like magic. A lot of missions tell you to "take out Boss X and all of his guards," which means you need to kill everything in a mission, but there are some that say "take out Boss X," and allow you to win without worrying about the guards. In a case like this a Stalker can turn on Hide, run to the boss, and kill him in one or two hits to complete the mission and then port back out to safety. Again, I think this is a really cool, thematic thing for an assassin class to be able to do. It's balanced by the fact that you don't get any XP for the guards you bypassed--only the boss XP and the mission bonus. If you use the newspaper and do enough such assassinations, though, I think you might be able to keep up a pretty good rate.