For standard of living, I'm mostly concerned with citizens at this time. While I don't mean to erase their plight, I'd like to keep African American slaves and indigenous Mexicans out of the discussion.
In 1800, Mexico’s per capita GDP (in 1950s US dollars) was $73. This was 2/5ths that of the US.
By 1830, Mexico’s per capita GDP had shrunk ($56 by 1845, $49 in 1860). By 1860, Mexico’s GDP per capita was 14% of that in the USA.
By 1830, Mexico’s population was (finally) growing. The demographic catastrophe caused by epidemic diseases coming from the Columbian exchange seems to have bottomed out around 1650 at a population of perhaps 4m. (All Mexican population statistics before the late 19th century are dubious estimates, and highly disputed.)
Some previously epidemic diseases seem to have become endemic by 1650 in Mexican Indigenous populations. Endemic diseases are still deadly, but they tend to kill children (the adults being survivors who have acquired immunity) and are less devastating to population levels than recurring epidemics.
Mexico became characterized by high birth rates (over 8 children per woman) and low life expectancy (circa 16 years average) due to very high child mortality. Still, the demographic catastrophe reversed, and the Mexican population began to slowly grow, reaching perhaps 5m by 1800.
In the 1790s the Spanish government instituted a policy to try to inoculate the entire population of its American and Philippine territories against smallpox. Perhaps due to this initiative, the population of Mexico began to grow faster after 1800. The population is estimated to have grown to 8m by 1855.
http://www.hist.umn.edu/~rmccaa/mxpoprev/cambridg3.htm
The population of Mexico was now growing faster than the economy, so the GDP per capita was declining. By 1830, the industrial revolution was producing growth in the European and the US economies, but it had not reached Mexico. The conditions conducive to industrial growth are said to be;
the availability of low-cost transport,
a relatively even distribution of income,
highly productive agricultural sectors,
low entry costs for early manufacturers,
the development of legal institutions designed to protect property rights and facilitate commerce.
None of these conditions existed in Mexico in 1830, with the lack of any transport systems which could facilitate the growth of a national economy being perhaps the greatest barrier.
If we estimate that the population in 1830 in Mexico might have been about 6.5m, and the GDP per capita might have been about $65. This would compare to a US population (in the 24 States which existed at the time) of 13m (from the 1830 census) and a GDP per capita of $325 (estimated from the previous source claim that Mexican GDP per capita was 14% that of the US in 1860, and using 20% on the estimated $65 Mexican GDP per capita) (all in 1950s US dollars).
So, the US GDP in 1830 is estimated at $4.2b and the Mexican GDP is estimated at $0.4b (in 1950s US dollars).
This would put the US economy at about 10 times the size of the Mexican economy in 1830.
The standard of living in the US was about 5 times better than in Mexico in 1830.
The military strength of both countries in 1830 was probably very little. The US maintained a peacetime army of just under 6,000 men in 1830, and a small navy. The Mexican army was probably slightly smaller as was the Mexican navy. The US obviously could mobilize more military strength from its larger population and economy than Mexico could, but neither country maintained much standing military in 1830.