So you have two cabs both loaded with two speakers of the same pair in each, one is and 8 ohm cab and the other is a 16 ohm cab.
Will they sound the same running at the proper amp setting?
PS: one might be wired in parallel and the other in series.
Will they sound the same? "Probably not."
Running the amp at 8 ohms means you are not using the full capability of the output transformer, which is obviously also capable of 16 ohms. The amp will react ever so slightly differently, probably.
Even if not that, as noted you have differently rated speakers in each cabinet. A 16 ohm speaker has more voice coil windings and probably bigger magnet, and that may impact the build of the housing etc. I would also wager that an 8 ohm version of a speaker model has a slightly different impedance graph vs the 16 ohm version. Not miles difference, but a difference.
And on top of that, you have two speakers in parallel vs in series. Speakers are never perfectly matched, just very very very close (usually), there's got to be some almost imperceptible difference in their physical build (tiny variations in voice coil wire thickness, different magnetic field form the rare earth materials), so the parallel set-up will cause one speaker to react a bit differently than the other because their impedances will play differently - you'll get ever so slightly different current flows through each speaker. The series setup causes each speaker to see the same current flow as the other (only one "pipe"), but the other speaker is "in the way" of the voltage, so they see only half the voltage - but again, not perfectly, because they are not truly identical.
For everyday purposes, I bet you could hear the difference if you really wanted to pay attention.
But I would also say: just rock that amp & speaker cab!