Is it faster for a U.S citizen to get married in Mexico and then do the I-130, or to go through a Fiancé(e) petition?
USCIS has a pretty decent page showing current processing times. Depending on where you have to submit your application for either one processing times may vary.
Long story short I would consult an immigration lawyer before doing one or the other.
Once your fiancee enters on K-1 visa, he/she will need to file AOS after the marriage to change status to permanent resident. That would end up being almost an identical process to getting the K-1 visa, which means you'll go through basically the same process twice, sequentially.
If you marry in Mexico and apply for IR-1 visa you'll only go through the process once.