I honestly rarely bother with the boars, the tamed ones will still give the same amount of drops as the wild ones so normally i just find myself hunting the wild boar. The more stars a critter has, the more drops it gives though, so yeah, 2 star is preferred if you are going to farm boars (but those tend to spawn in areas farther away from spawn, so not something you tend to get super early anyway).

Worth noting the same logic does apply to the other tames though, and if you can survive things like the deathsquitos (serpent shield ftw) you can tame stuff like lox WAY before you are meant to by just leaving some cloudberries around where they already wander (which is usually between patches of cloudberries as is). Stuff like that can be totally worth taming, because you can end up getting some plains materials super early (not only is it much easier to kill a lox that doesn't want to murder you on sight, they are also great about killing everything remotely near them to, except they get nuked by the squitos surprisingly often if they are just 0-1 star)