Interesting concept. I think the game is best played in 3x3, but with alternate rule that player 1 must start with circle and player 2 should be able to use any shape from the start.
For 4x4, when played defensively, neither player can win.
EDIT:
By defensive I mean attempting to remove opponent's pieces.
I just played several more rounds. When played correctly, Player 1 is guaranteed to win on 3x3 even when all pieces are allowed from the start for player 2. Player 2 simply cannot "defend" against a center circle or a corner circle.