Utah is only about 50% LDS now, so some of those battles they're unlikely to win based on religious grounds. Both schools will continue to lose top-ranked recruits to the likes of Oregon, USC, and Washington, too.

So if you have 10 recruits, and two go out of state, leaving 4 LDS and 4 non-LDS kids, it seems that BYU is more at risk to lose an LDS kid to Utah than vice versa. If BYU and Utah were equal strength programs, with equally good coaches, recruiting, etc., then I'd still imagine BYU would only average about 3 of those top 10 in-state recruits per year, Utah 5, and the final two headed elsewhere.