Love my Tascam US-16x08, so I'm biased.
Both of the units you're considering can be powered separately, and not just from the USB buss, which is great, but...
One difference I note is that the Tascam takes a standard DC power plug & brick, while the Steinberg uses a second USB port. I think that makes the Tascam a little more flexible. My Nektar P6 has 2 USB ports, one for communicating and one for power, so that ties up 2 ports on my PC. I happen to have plenty (6 USB2 and 4 USB3), so not a problem for me. Just something to be aware of.
Drivers for the US-NxN series are developed and supported in-house by Tascam. Maybe Bob can clarify the driver development for his UR22.
I really like the Tascam preamps, and I especially like the fact that the mains are buffered on power up/down. No pops, if I forget to turn my monitors off first. I'm assuming that the US-2x2 has the same buffering. That is worth something to pre-Alzheimer's me!