Symmetra damage: 30/60/120 per second (Goes up a level each second, falls off after three seconds without dealing damage)
Winston damage: 60 per second
Symmetra health: 100+100
Winston health: 400+100

Mind that Winston is far more mobile than Symmetra and can thus run or stop Symmetra from running as he feels like.

Winston can kill a full health Symmetra in 3.3 seconds.
Symmetra can only do a little more than 250 damage in that time, which is only half of his health. He disintegrates turrets extremely fast, so he'll probably be healthy enough after destroying them to beat the Symmetra unless you have good enough team coordination, which isn't that common honestly.

Winston's gun is pretty much the best way to clear Symmetra turrets in the whole game, and he can beat her in a 1v1 to boot.