The difference, by the numbers
They have no ingredient in common: the Lemon, Lime and Bitters has lime juice, lemon-lime soda and alcohol-free aromatic bitters, the Virgin Mary tomato juice, lemon juice, hot sauce, Worcestershire sauce, horseradish and Tabasco, celery salt and pepper. In parts, a Lemon, Lime and Bitters is 1 lime and 10 lemon-lime soda; a Virgin Mary is 10 tomato and 1 lemon. By volume, the Lemon, Lime and Bitters is 91% mixer and juice and 9% citrus; the Virgin Mary is 91% mixer and juice and 9% citrus. Different bottles, similar balance: that makes them close cousins on the ratio map.
They are about equally strong in the glass (both 0.0% ABV), and they hold about the same alcohol (0.00 standard drinks each). The Lemon, Lime and Bitters has more calories (about 68 against 31) and more sugar (16.5 g against 4.5 g). Both are served in a highball; the Lemon, Lime and Bitters is built, the Virgin Mary stirred.