Taking Apple's 20% claim at face value:
Geekbench Single Core - M1, M1 Pro: 1700, M2: 2040
Geekbench Multi Core - M1: 7700, M1 Pro 8-core: 9000, M2: 9200, M1 Pro 10-core: 12400
Of course we'll see M2 Pro/Max sooner or later, which will presumably match M2 on single core just like the previous gen.
Which you shouldn't. They are, once again, using performance per watt. Nothing guarantees that it even runs at the same wattage.
If the M2 has 18% higher PPW, and keeps the same TDP / power draw, that's 18% higher performances (remains to be seen whether it's across the board for E-cores, or for P-cores) it's about 25% below the 6+2 M1 Pro, and about 70% below the 8+2 M1P. At least looking purely at the CPU.
The M1 Pro is a 6+2 configuration, so it will have a little bit of an edge in core configuration, but Apple claims 18% faster on this generation, which might cancel out that edge a little bit (I'm guessing slightly slower still, but close). The M1 Pro does have a 40% larger GPU, but the M2 is 35% faster (again, taking Apple at face value) so it should again be similar-ish in gpu performance, very slightly slower (135/140 = 96% as fast).
The big difference is still that M1 Pro gets support for much larger memory, and the 14" has a much better port configuration, the 13" is basically still the same old chassis with USB-C and the touch bar, just updated with a newer processor.