Many of the proposed new designs use higher enriched uranium, with up to 20% U-235. I expect that if they could work with 5% they would, but they can't. So from here I conclude that their waste might contain a much higher level of U-235 than the current PWRs, for example 3-5%. This would make it good for burning in a PWR, but of course, you need to first clean it up, and that requires processing.