Kaliforniahunter93,
First off, you have made a good choice on the Encore. These are excellent guns and will provide you with many years of shooting and hunting.
If you've already "zeroed in" on either the 270 or the 308 I'm certain either will easily handle the coyote. I'm not familiar with wild boar, but from what I have read on those little pigs, either caliber should take those with no problem as well.
Barrel??? Well, if your going to buy the ProHunter frame, then the matching barrel is nice. If your going to buy the Encore frame (non-prohunter) then I would just stick with the Encore barrels. The Encore barrels are just as accurate. I agree with Grumlkin. I like the heavy "bull" barrels myself.
Back to calibers....Do you handload? If you handload I don't think you could make a bad choice. You could really load any type of bullet (Ballistic tip or expanding) in either cartridge, and there are enough different powders to speed 'em up or slow 'em down. If you don't handload, you may want to stick with the 308. You may have some more ammo choices there. Just go to any online ammo place and scan the selection.
Hope this helps.
Either way it will be tough to make a bad choice.
Dave