To me the story was a minor bonus (and more interesting if the hidden meanings are explained), the game can be played for the puzzles and artwork alone. Also the paintings you were assembling are kind of interesting, I wish I could figure out how they fit into the story.
[Argh! Me and Braid, we go way back. I hate it with a fiery passion because of the pretentiousSpoilerstory. I can appreciate the gameplay, but the hate still burns with the fire of a thousand suns.
If we're talking strategy, I nominate Combat Mission : Shock Force, the most realistic tactical wargame available, check it out.
BG&E, I agree is a great game, but I feel it gets too much praise. It's like a combination of Thief 3 and Oddworld: Munch's Odyssey, but both of those games are much deeper and more deserving of praise.