This question has been answered conclusively for the the competitive skeet shooters. They all shoot tubed guns as there are undoubtedly some advantages to that system. However, NSSA skeet has always done all that it could to make that game "easier" which is totally unlike the Olympic Skeet variant.
As for me, the separate appeal of different guns would be my preference especially since I don't try to compete in any target sport anymore.
26If you use tubes, the weight will vary, as will the balance, but the feel of the forend and grip remain the same, as does the trigger pull.
OTOH, if you use separate guns, but all the same like for instance, all Browning 725s, then the balance will be closer to the same, as will the grip and forend, but the weight will vary also.
If it were me, I'd probably go with tubes if I were competing.
Having said that, I shoot skeet every week using a Browning 725 in 20 gauge with 32" barrels and a Browning field grade Citori in .410 bore with 26" barrels. Very different in terms of weight and trigger, but close enough to make me happy.