So sad, since there are so few great two player games. I was really hoping this would be one of them.
I would disagree with you on TS, as it is one of the simplest two player games with any depth I have ever played. My wife owns a game store; I have played a great many two player games.
I love to play Coloretto, Battle Lines, Hive, and lately Innovation.
For both types, card sets with little interaction usually have one or two good strategies, and luck plays a large-ish role in whether you or your opponent(s) can execute the strategy faster.
Card sets with more interaction are IMO strategically more interesting with more than one opponent. Usually, everyone will focus on keeping the strongest player from winning, who in turn gains less from further weakening a single opponent already weaker than him. In 2-player games, the stronger player can just lash out at the only other opponent, which directly increases his chance of winning.
So the chance of turning a game around after half the time played is much slimmer in a 2-player game than in a 4-player game, from my experience.
Anyway, Dominion is a great game that packs a lot of strategical depth in a rather short playing time!
Do you have any specific examples of how this happens? One of the design goals of Dominion is that there are no "kingmaker" mechanics, so you never have a choice of which player to attack or help. Cards that allow interaction usually target either the player to your left, or all other players.