I think what attracts Tony to animals in general and Pie-O-My in particular is their loyalty. Sure, the ducks left him, but only through the family tie they held within their own unit, which he admired (their flying off induced an unconscious fear for loss of his own family).

Tony yearns for loyalty; he did before, and particularly after, Pussy's betrayal. His first real rant in the show is to Melfi, about how people take the easy road out now and become federal witness and all that. With animals, you get loyalty, and somebody to talk to even. They may not talk back, but then that's an advantage, because when somebody talks back to Tony, it's usually to nag at him (Carmela) or add to his general stress levels (be it Janice, Junior, AJ, Meadow, Chris or Paulie at that time).

There is perhaps more to it; that Tony admires the animal's physical finess, its structure and how graceful it is and how beautiful it is. The horse can at times be very ferocious, but only when it isn't treat right--like Tony himself, perhaps?

Thanks for reading,
Mick