Apart from having a larger cooling surface area for dissipating heat? Not a lot.
The GTX-1070 is an excellent card with great thermal efficiencies and performance compared to older GPUs.
Small-form variants of this card look really attractive to me for HTPC use and for mini-pc builds.
Most of the mini-GTX 1070s I've seen so far have the same base and boost clock speeds as their bigger brethren and some overclock reasonably well to boot.
Since they usually have the same amount of DDR5 memory (8Gb) and port outputs as the bigger ones and occupy less space in the case, there are few, if any, disadvantages as long as you have a well-ventilated case.
