The OP posited two players, each rated 1200 at their time controls, and asked which might be the stronger player. Ignoring the obvious answer that each would probably be stronger in their familiar environment, it is likely that the player who spends about twice as much time per move would have learned a little more about the game than the speed player.
At 1200, I think you'll be right. At 1800 or 2000, perhaps the 10/0 player may be the stronger. What do you think?
Hard to tell. If the 1900-rated blitz player was a strong player who plays a few fast games for fun once in a while, then yes. If the blitz player learns a lot of opening traps to catch people off guard, has pre-moves for many of his openings to save time and has just concentrated on playing as quickly as possible, then no.
The OP posited two players, each rated 1200 at their time controls, and asked which might be the stronger player. Ignoring the obvious answer that each would probably be stronger in their familiar environment, it is likely that the player who spends about twice as much time per move would have learned a little more about the game than the speed player.