If you are just looking for a dedicated yote/cat trap....a 650 is an awesome trap. Big pan, big trap. IMO they are too big for fox and coon. You can adjust the pan tension on them with a turn screw. So you can set them to catch fox and coon. But I don't think it would be pretty. Due to the size and no loose jaw, a little harder to bed. I can't set a 650 over me knee. They make setters but I think they are dangerous if you loose your grip on them, I have heard of guys getting smacked by them. I set 650's on the ground which is fine if not too much mud or snow. I only use them if I am targeting yotes or cats without concern for fox and coon, and where I am confident stray dogs won't be an issue. If you are only looking to catch cats and yotes, and don't mind spend a little more time making each set, then 650's are the ticket!
The 550 is a lot easier to set, I set them on my knee. I recommend the 2 coil. It will hold a yote no problem and is a better trap for a mixed line. They bed more easily due to size, loose jaw, and the trap frame. I have used the offset 550 and the rubber jaw a couple times as well. The rubber jaw will probably hold coon better than the offset, but I have had some coons pull out of the offset. The pan tension is a little stout for grey fox although you can catch them some if not most of the time. They catch reds no problem. I use the 550 a lot and it is a great trap. I am moving more toward the 450 because of coons and greys, but they don't make that in a rubber jaw.
Might be a good idea to get a couple of both and see what you like. They are great traps.
Speaking of stray dogs, I highly recommend getting a catch pole. Makes it a lot easier to release strays.