In my experience, the turn is hardest street to play. If you've been paying attention, the flop is all about figuring out things like how wide his cbet range is and things like that. The river should be pretty clear if you played the turn right. For instance, it's an odd bird that is bluffing with cheese on the river. But the turn... that's where poker is played. That's where the bluffs happen. That's where made hands are either pushing out draws, setting fishtraps, or opening a mine in Valuetown.
Obviously it's based on things like the strength of the hand, the action in the hand up to that point, the texture of the board, the history of the opponents play, your table image, and a bunch of other factors like that, but I would think of all-in on the turn as common and more often correct than a shove on the river in the same situation.
Food for thought: If you're complaining about finding yourself in the situation you laid out (remaining stack
ot size = 1:1 on the turn) you may be a little too passive, a bit too loose, or chasing. It sounds like your tables have multiple callers, which you should be probably be attacking more aggressively, or you're one of the callers looking to see more cards for cheep and end up getting deep into the hand with some wide holdings. Just sayin'