The history of Cherokee is very similar to that of Homeline, except that religion played a much greater role in the treatment of Native American tribes, with the end result that instead of being marginalized, they are the key political and economic players throughout the Midwest and West United States. The Cherokee in particular dominate Big Oil and vie against the Arabs in OPEC in constant economic competition. The recession and gas shortage of the late seventies didn't happen, with the effect of having much closer Presidential races throughout the eighties, but no other significant historical effects have been found. There are a few cultural differences - tribal facepaint is common among corporate executives of all nationalities and specialties, the interstate highway system is less extensive but more broad (10-lane freeways are the norm, but there are far fewer of them), and, despite New Agey theories, pollution problems are pretty much the same.
In general, you can expect Texas and the southern Midwest to be much richer and more cosmpolitan, but other than that, Cherokee is identical to 1986 Homeline.