Physics. It's terrible on consoles.
AI. It's hard to program but the majority of games still being made have just awful AI.
Loading Times. Sony went with a 2x Blu Ray drive in PS3 which was great....for 2007. 9MB/s isn't cutting it when the majority of disks have 50GB, while some that use Single Layer are still 25GB. Go with at least 8x on next-gen (both PS4 and 720)
Updated Blu Ray optics. Support the quad-layer 128GB disks. Technically nothing needs to be done, but use the updated optics to be sure you support it. That's future proofing, it holds 7 hours of 1080p video, or 3.5 hours of 4K video.
Bandwidth. Not internet bandwidth, silly. Internal bandwidth. Current consoles use GDDR3 which for modern graphics is just too slow. Then they use 128-bit bus. Too narrow. Consoles will need either 256-bit or 384-bit buses with GDDR5 VRAM in order to feed the GPU. Anything below that, and the card will be starved of bandwidth.
