Well the Alamo was 10 years before the Mexican American war, but ten years is not a lot of time in the flintlock era for guns to change. Plus remember that many of the 3rd models captured at New Orleans found their way into State armories, and also into civilian hands and that was the War of 1812.
The Bess of the Mexican Army was the 3rd Model, and was probably the weapon used by that army when engaged in some fighting with Americans. Unfortunately, some of the engagements in California, were United States forces, including Marines and sailors, against Californios..., locals of Mexican descent who were loyal to Mexico, and their largest force was of 600 Lancers, a la Napoleon, with very few firearms.
In the Battle of Rio San Gabriel January 8th 1847, and the Battle of La Mesa, Jan 9th, 1847 it was the Californios with a piece or two of artillery vs. United States infantry composed of Marines, Sailors, Soldiers, and some locals.
One account of the action at La Mesa claims the Americans won because they inflicted heavy casualties on the Californios as the Americans were "armed with rifles". I think that is just plain silly, as the American forces that day were the same as on the day before at Rio San Gabriel, and no mention of rifle fire is made at the battle on the 8th. Further, the lancers to attack had to close with a charge, and had the Americans been using rifles, fire would've been opened on the Californios from a distance..., the casualty rate would've been much higher.
The few Mexican soldiers probably had the 3rd Model Bess, the company or so of American volunteers could've had them, too. As for the American regular forces, they probably had one or more variations of US muskets, which were derived from the French patterns of the previous century..., or they had pistols and sabers, for there were dragoons among the American forces.
LD