I'm using them both side by side, it's noticeably faster (S22 Ultra) when running games vs the S21 Ultra. The system feels smoother on the S21 Ultra however, but I'll hold my reservations until my S22 Ultra settles in, after all its just my first day of use. On a positive note, it took me less than an hour to fully charge my S22 Ultra using my 45W Samsung charger!
Some other notable improvements are that apps aren't taking as long to install from Google play as they were on the S21 Ultra.