It's getting hard to tell the difference, other than different floorplans.
Go to the Heartlandrvs.com website, select the Big Country, and select the
Standards and Options page, print it out, and then do the same for
Bighorn. If you go line-by-line you'll find some differences. But you may want to check further on anything that's important to you, because if something's on one and not on the other it doesn't always mean it's not there. If may have just been left off the list.
If you call Heartland Customer Service at 877-262-8032 / 574-262-8030 and identify yourself as a prospective customer, you can talk to the Big Country or Bighorn Brand Manager or one of his people and they should be able to spell out the differences. You may find that many of the differences are subtle; like the way the slideout controls work, or the wiring for satellite receivers. Exterior appearance can sometimes vary quite a bit. Air conditioning ductwork may vary. There are a lot of variances across different floorplans and across brands.