MrBankRoll: the best tasting tomatoes are "heirlooms" such as the Brandywine varieties. However, the fruit often grows erractically. Big tomatoes seldom ripen evenly. The best opportunity for ripe tomatoes is to clear out the middle, as full sun is the most important factor. Also roll some cattle fence and your four footers will comfortably become eighters.
However, if what you what is solely big tomatoes, then you have to reduce the amount of branches and even pinch off some of the blossoms. You can pluck off the internode branches (commonly called suckers) or you can pinch back the main stems and let these grow outward.
Tomatoes like water, but not wet feet (soggy roots). In the future, soften the soil with some sand before planting. A wide variety of garden pests favor tomatoes. I long ago eliminated slugs, by providing excellent nesting areas for toads. For one rather large garden, a number of years ago, I paid a couple of young boys to apprehend some toads down by the marsh and bring them to me. With cages and thus keeping the fruit off of the ground the problem of mice and voles become almost nill.
Yet the main purpose of large ripe tomatoes is to make tomato sandwiches and to eat them with a huge grin. We demand photos.
"When in doubt, empty the clip."