Is there much strategy and planning in 7-Wonders or is mostly luck?
7 Wonders is a very different kind of game than Race or Dominion.  Race &amp; Dominion are both "group solitare" games.  By that I mean that there is little one can do to affect one's opponent.  The game is mostly your own strategy.

7 Wonders is strictly an "adaptive" game. You cannot go in with any kind of strategy; even choosing wonders is random according to the rules.  Every decision you make affects all other opponents, neighbors more than the others.  If you don't take that into account, by, say knowing "I'm going to pass these 6 cards, and I know my left neighbor will likely choose this card, so I should choose to do X", then yes, the game will feel random.

My biggest criticism of this type of game is that weak players give other players big advantages.  If you want to enjoy 7 wonders, play with people who know the game well, start thinking about everyone's tactics not just your own, and stop worrying about strategy.