In as simple terms as possible, conventional grain films have "round" crystals, and T-grain films have "flat" crystals, a bit like floor tiles. Because the T-grains have a larger surface area for the same volume, they are more efficient in gathering light, and in theory more economical to manufacture because the volume of silver is reduced. Such films include TMax 400 and 100, Fuji Acros and Delta 100 and 400. The three main manufacturers' T-grain films are similar but certainly not identical, as they differ in their spectral response, grain shape and size and tonal curves. Someone who knows what he is doing might develop them to appear indistinguishable, though, as the tonal curve is highly adjustable through development techniques.
T-grain films are better in some ways and worse in others. They look less grainy. They are more sensitive to temperature during development, so the standard temperature compensation chart doesn't work for them. They do not render fine detail, especially in the highlights, as gracefully as conventional films. But it takes a trained eye to see this, and for most it won't matter anyway. I would use any of the current films available, T or not, without worrying too much about it. My own preference leans towards TMax 400 and Acros for 35 mm, and FP4+, HP5+ and TriX for medium format, with grain playing a role in the 35 mm decision. Even so, I have no innate resistance to loading TriX or HP5+ into a 35 mm body, if that is all I have available.