I've heard the .357 magnum Desert Eagles can be finicky, but the .44 Mag and .50 AE ones seem to work great. That said, the big bores are a bit much for HD I think, in my local anything .50 bore and over is considered excessive force even if used in a "good shoot", so I'd buy a .44 Mag gun if I were going to buy one. The ammo is also MUCH cheaper.
Anyway, I'd rather have a rifle for HD, I keep a Kalashnikov for the purpose, you could do worse than a Desert Eagle.