Strictly efficiency-wise, I'd expect them to be about the same - if by efficiency you mean the ratio of heat produced to wattage consumed. They're both basically just big resisters stuck in a circuit. With light bulbs, the difference in efficiency between incandescent and LED comes down to the fact that light is what you want out of it and heat is wasted energy. Both types emit both visible light and heat, but incandescent bulbs produce a whole lot more heat for the same amount of light, and that's where the efficiency difference comes from.
In a radiant heat panel, all it produces is heat and all you care about is heat, so the only waste is heat that escapes the enclosure. The biggest reason a RHP is more efficient than a lamp in a fixture above the cage is that most of the heat that lamp produces gets lost to the room and doesn't make it into the cage. An RHP is all the way inside the cage, so there's less loss.
So if you want efficiency, put lots of insulation on top of the enclosure so you don't lose heat through the ceiling. The brand of heat panel won't make much difference in efficiency, but insulation will.