If you ware looking to improve your TvZ and are in a low league, I would suggest that you play mech because bio is mechanically demanding - and a players lack of mechanics can just lose them the game in certain engagements - while mech is so much more positional/strategical. When in Plat with terran I would not do any fancy mech play (battle mech is mechanically demanding - hence I would term it as fancy mech play) but just the stock standard: make hellions, tanks and thors. And when you go to late game against zerg with mech, you can transition into Thor-Liberator or Battle Cruiser-liberator-raven. With OK macro and a proper build order you will be able to get to D3 with terran.
In regards to your statement that your zerg opponent is on their 10th base while you are on your 4th, I would suggest that you have a major strategic/build order problem because (from personal experience) in these lower leagues your zerg opponents do not have the mechanics nor the knowledge to exploit the advantages that their race provides them with, and this allows a passive terran who is following a build order and hitting their production timings can just outgrow their zerg opponent (in a recent game I had with my account as I played on Korea, I was able to get a maxed out mech army while my Plat Zerg opponent only had 100 supply).