It kind of depends on what kind of conservatism you're referring to.
If conservatism means strict adherence to tradition and deference societal institutions, it's indisputably BYU. Most of its students and faculty are members of the LDS Church, which is arguably the anchor of Utah society, and faithfully follow its doctrines regarding things like missionary work and the promotion of early marriage and large families.
If conservatism means Right populism with the end goal of ensuring that a privileged group in society maintains said privilege, then A&M is the winner. Aggies are not "conservative" in their behavior in the way BYU students are - they can drink anyone under the table and aren't partaking of any less sex and drugs than their liberal adversaries in Austin are. But A&M is very much about preserving the "good old boy" network in Texas -- the reason you'll probably see a lot of maroon-colored paraphernalia in the executive suites of many a Houston oil company. They're the Rick Perry to BYU's Mitt Romney.
I'd argue that they're both about equally conservative in their own respective ways. BYU represents, to put it in a Forum context, a "DC Al" sort of conservatism that is about adhering to established rules and morals. A&M offers up more of a "Cathcon" conservatism that involves white males engaging in law-breaking, libertine behavior while defending their white male privilege.
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