Edit: Wings of Liberty answer only, this is outdated in HotS!
The most used tactic when you go bio vs his siege tank push is to flank his siege tanks with stimmed marauders, stutter stepping towards their dead zone as fast as possible while still shooting.
You want to apply pressure from the front at the same time to force his marines in a defensive position in front of the tanks, otherwise they'll just kill your marauders off.
If however you went mech, simply having your siege tanks sieged up will zone his siege tank push enough to force him to make the first move, thus taking more damage. He'll most likely try to flank you, so be prepared to deal with it somehow. You'll want to mass enough vikings to zone his medivacs (denying his vision) and provide vision for your tanks instead, and to expand behind your siege tank line to get enough resources for a skyterran transition (battlecruisers with raven and viking support).