I once was lucky, when I swapped woofers in a SWR 212" (ferrit, 8 Ohm) to neo woofers with a total impedance of 4 Ohm. The cab sounds great, but it didn't get any louder, lets say, its not hearable. But I was able to use the cab with some all-tube - heads that don't accept 8 Ohm.
This time I bought a BenzBenz NeoX T 212 (4 Ohm), and it seems like the former owner did stress the cab too much. In some setings you hear the cab overexcursing - at living room levels. So I asked agedhorse, but there are neither reconing kit nor two replacement speakers available. I found some speakers that should do it, but they will reduce the impedance to 8 Ohm (2 x 16 Ohm). Agedhorse recommendet not to go that way, but rather take two woofers from the same manufacturer GenzBenz used, but not the OEM version GenzBenz mounted. Because they are no longer available. I will take the stock models because the difference is not that significant, the OEM - modell just had a different mid voicing. This is what EQ are for.
I would mount the given speaker into the cab whatever BagEnd recommends. They maybe used OEM - speakers with a different voicing and know best, what suits the cab.
Otherwise changing a cab to 4 Ohm does limmit the number of cabs you are able to use. Remember, you should not go under the given impedance of the amp. So when your amp says "minimum 4 Ohm", you don't want to let it drive two cabs with less than 8 Ohm.
Next point: 8 - Ohm -cabs are better controled by the amp. The cones get damped better, this helps for a better articulated, punchy sound.