Taylor had far more military experience than Lincoln or Grant. I'd say Taylor wins the year in about four and a half years. More recently experienced regulars from the Mexican-American War may very well help turn the tide. If Sam Houston and Robert E. Lee keep Texas and Virginia from seceding, even Kentucky and Missouri seceding wouldn't make up for it. The popular sentiment would encourage moral among the regulars, and I imagine that Taylor himself may resign the Presidency to help lead the war. At the very least he would probably be a much better military strategist than Lincoln.
The majority of U.S. troops in the Mexican-American War were Southern volunteers, not regulars. That said, with Abolitionist sentiment far weaker, you wouldn't get as much of the South to secede.