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for example, they seem to have exactly opposite philosophies about taking the bar out of the rack, arm angle, and range of motion
what? taking the bar out of the rack? what does SS really say about that? it sure doesn't say to let your shoulders come loose on the bench. arm angle is more tucked in tate's but SS leaves this aspect of the lift pretty wide open. hard to say they have exactly opposite philosophies. range of motion? from the top to the bottom, where the bottom is defined as touching the chest. that seems the same.
tate, imo, exaggerates the bar moving back when he first talks about bar path. watch at 8:20, though. he's not talking about bar path, and it moves pretty much straight up and down.
so i don't know what you're saying. basically use tate's video for understanding how important it is to keep your shoulders low when you unrack and stay very tight throughout the lift. where your elbows end up varies, just make sure they're always under the bar. foot placement is not terribly important, either.