While prices at the duty-free shops at the international airport aren't fantastic, and aren't as good on booze as in the USVI and some other places in the main Caribbean, certainly prices on booze are lower than almost anywhere you'd see in the U.S.
I think Jack Black in the liter (not fifth) size was US$13 or so in August, and in the U.S. it would be US$20-$25. Plus sales tax in some states. Scotch and other imports from the UK are also significantly cheaper than anywhere I've seen in the U.S. or Canada.
I also paid just US$4 a fifth for my favorite Belizean rum, Duurley's, which is a little cheaper than I have seen it elsewhere I've seen in Belize.
Prices at the several duty-free shops do vary a little from store to store.