Lol i played every race. T is like the sheik of sc2; they are very versatile in both offense and defense and they have lots of different builds. P is kinda like peach; you have to know exactly what you need to do at every second, your army usually wins in straight fights but your weakness is mobility. Z is like falco; it once was the case where you could kill them early but Z players have learned to avoid it and their biggest strength is map control.
I just switched from P (my first race) back from Z (who i've played since last december). PvZ is very strange. P can't be aggressive early any more since the 4 gate was nerfed, so zergs can sorta expo once for free. Because of that, protoss have started going forge fast expand, which makes the zerg take 2 bases early. The standard followup after for P is to go air and try to deny the 3rd base. This is sorta the engagement that determines the pace of the rest of the game. If P does well harassing, they are able to secure their 3rd fairly safe and tech. If Z shuts them out, Z can delay P's 3rd for such a long time that P is almost too far behind to win. And yes, infestors are pretty strong; infestors basically make zealots and sentries useless, but collosus/archon/stalker is still really hard for Z battle straight up so its pretty fair.