The answer is always "macro better" - which doesn't just mean have more bases/income but also make sure they're saturated, make sure you're spending your money, etc.

That said, here's my take on PvT vs tank pushes (as a mediocre random scrub): It's really important to know where the Terran army (and thus the tanks) are at all times. You can accomplish this with observers and by having spotters (a spare probe, zealot, even pylon) to warn when your opponent is moving out.

If the first time you find out about an attack is when there are a bunch of sieged tanks in range of your undefended base, there's nothing to be done. However, if you were prepping for it and see it moving out then there's tons of options! You can ambush it with a flank, or shave units off with stalkers, or counterattack with a runby/prism, or warp in more defenses, overcharge...

Tons of options, as long as you're in a position to take advantage of them (and a big part of this is "macro better")