I would rather have the winch. Pulling anything with a come always sketchy, and you're right there if something breaks. There are so many cheap winch options on the market today, that are more than adequate for occasional use.
Either way I would go with webbing straps over chains. You need at least a strap to keep from damaging the tree.
Rigging SWL should match or exceed the winch/come along rating. So a 4000 lb come along should have 4000 swl chain/strap. That would be something like 5/16" or larger in chain. All shackles, hooks, etc should have a similar or greater SWL.