I think Little White Pet was called a polyantha because people didn't know what else to call it. Re "Lewes Kell": I haven't seen it repeat. Pat says it's more vicious than F-P (and I agree with that, having taken cuttings of both recently).
'Félicité et Perpétue' will have the occasional flowers in September especially if it is pruned back a little after flowering, which it will need as it has a very irritating habit of hanging on to its dead flower heads. 'Little White Pet' does the same. In Sussex I grew two 'Félicité et Perpétue' on chalky well drained soil on both the east and west side of a wall. In Devon 'Little White Pet' grows very happily in my acidic loam, there is almost never a time when it is not in flower from mid-June to October. Both roses were very healthy.
The leaves of 'Félicité et Perpétue' and 'Little White Pet' are noticeable because of their dark green colour, 'Lewes Kell' looks a little bit paler. And the stipules on 'Lewes Kell' are smooth whilst on 'Little White Pet', at least, they are slightly cilate.