Using the information on the Mac Pro specification page and the Intel ARK processor database, it's likely processors in the new Mac Pro are the Xeon E5-1620 (4-core), Xeon E5-1650 (6-core), Xeon E5-1680 (8-core), and the Xeon E5-2697 (12-core). Poole's benchmark estimates for each can be seen in the charts below.
The upcoming Mac Pro will have significantly better single-core performance than the current Mac Pro. For example, the upcoming 4-core model will be between 50% and 75% faster, and the upcoming 12-core model between 16% and 32% faster, than the equivalent current models. Multi-core performance is also significantly better. The upcoming 4-core model will be between 58% and 78% faster than the current 4-core models, and the upcoming 12-core model will be between 17% and 47% faster than the current 12-core models. The 6-core and 8-core models are also quite speedy. The upcoming 6-core model will only be 10% slower than the current base 12-core model, and the 8-core model is faster than most of the current 12-core models.