They're both pretty active but in different ways. Flame Tetras are more a shoaling species, they do school loosely and tend to favor the mid-upper tank level. They tend to mix easily with other species, but are not hyper. Also know that they are little gluttons, and will out-compete other more timid fish like Pencilfish and smaller Rasboras.
Red Phantoms tend to school a little tighter and tend to stay with their own kind. The males, when well fed and feeling good, will spend hours doing fin flaring challenges which will have both of them laid over at the most ridiculous angles to each other. Compared to Flame Tetras, they're a little less active and tend to hold closer to the lower 1/3rd of the tank. But the Red Phantoms more than make up for that with the male threat displays.
I would get a school of both if I have the room.