It's my understanding that LEDs, PAR for PAR aren't more efficient than halides per say. The difference is that they direct light better. If you consider total light output, halides are still more efficient, but halides don't necessarily get the light were you want it, so, a lot is wasted that way. I should note LEDs are more efficient lumen for lumen, but this is a useless matric, you could have 20 lumens of green light and 1 lumen of blue light and exactly the same PAR. Lumens are weighted to the sensitivity of the human eye, which has nothing to do with photosynthesis.
I always use the rectangle example. If you have a square and put a halide over it, the halide will illuminate it well, as it's designed to light a circular area which is close to a square for most purposes.. If you put that halide over a rectangle, it won't illuminate it well, a lot of light will be wasted over the front or back, or you'll only illuminate a small part of it and then it may be low enough to cause heat issues. If you want to illuminate a tank PAR for PAR, with exactly the same spread as a halide though, on a square tank, you won't really get an improvement. Many people do see an improvement, but that seems to be more because their PAR numbers are lower (on average, not necessarily at the brightest area). If you light a rectangular tank though, you can basically double the efficient, just because your fitting the shape of the tank correctly. Many people do seem to do a bit better than this though. I think this is because, halides are roughly the same price regardless of wattage, so, people are using much more halides than they need, so, there is room to decrease this as well. Or people are using inefficient reflectors with their halides, such as parabolic "spider reflectors" etc...
This article shows the footprint of various lighting for example:
http://www.advancedaquarist.com/2010/2/aafeature2
As for heat, I believe LEDs still waste more energy as heat than halides, but the heat goes to the back of them, and the heatsink, where it rises and dissipates, rather than the front where your tank it.