I think it depends on why one wouldn't like third-party ownership in the first place. If it's a question of divided loyalties--as you see in Italy, where a club can be a third-party owner in a player at another club--then it's a distinction without a difference. In my mind, that's not really different from a loan.
If you look at it the way I think the EPL does, however, it's a question of financial stability. A transfer fee, essentially, is a capital outlay amortized over the life of the player's contract. Third-party ownership spreads that risk around, but it also makes it harder to sell if the club gets in trouble. If the story behind the Carvalho deal is true, his third-party owners wanted about 26M pounds for their 75% share, while Sporting were willing to take about 6M pounds for their 25%. Sporting is hardly hurting for cash, but if they were, they could get bent over and have to take maybe 2M to get the deal done. In that sense, the argument is similar to those against doping. Doping gives you the chance to compete (who wouldn't want Carvalho for 25% of his transfer fee?), but it has potentially scary consequences.
Since the English FA is essentially a puppet organization of the clubs, I also suspect they see third-party ownership as a way to suck more cash out of clubs in bung deals with managers and directors of football.
