It is an interesting question.One result doesn't define a season. We beat Arsenal, City, United, Chelsea, Spurs and the scousers, it doesn't mean we have a better squad than them.
I think the answer hinges on Stones and Lukaku. As we all know they may leave or they may stay. If we list the key players including these two then I think Everton have a much stronger core to the squad than Southampton.
Baines, Stones, Jagielka, Lukaku, Lennon, McCarthy, Barry, Deulofeu, Barkley, Coleman, Funes Mori. That is a strong base to work from and absolutely it does need at least another four or five top players to make it a squad that can challenge.
There is another consideration which Southampton fans are probably not aware of but certainly would appreciate ...and that is the quality of youngster coming up from the academy.
Southampton are as good as anybody at producing very good young players...not so good at keeping them however.
Koeman did say last season that there really were none up to the level of playing first team football and he was criticised for not giving youth a chance.
At the moment Everton are in a phenomenal moment of producing young players(to paraphrase somebody or other)
Browning, Galloway, Kenny, Pennington, Connolly , Dowell and Davies all got first team experience last season and some of these are very good prospects indeed.
It keeps being pointed out on this forum and to be fair most pundits recognised it last season that Everton should have done much better with the players available to the manager....after all that is why RM lost his job and I think it is also the reason that Koeman decided to leave one club and join another.
That is not to put down the Southampton players down in any way and there are a few we would love to have at Goodison.