Language differences of Mexican and Puerto Rican Spanish.
Not an easy one, you see, Mexico is a very big country with a big population, some 110 million people, and Mexican Spanish is an umbrella term that encompasses at least 10 different regional variants, meaning the Spanish spoken in Yucatán is at least a bit different from the one in Baja California or Mexico City or Monterrey.
Having said that, one feature common to most dialects of Mexican Spanish is the tendency to pronounce all of their consonats, so words like "libertad", which would normally have the "d" sound dropped in most of the Hispanophone world (libertÁ), will clearly have the final "d" sound, usually resembling the sound of the TH in THat or wiTH (libertATH). Other feature is, in informal speech, the reduction of unstressed vowels to, roughly, what English speakers call a "schwa", like the unstressed A in words like "about" or "around", thus making a sequence of words like peses-pesas-pesos-peces or paso(s)-pase(s), sound very similar, if not the same, just like, to me as an ESL speaker, "gorilla" and "guerilla" sound the same. I may add words of Aztec origin also make Mexican Spanish a very distinct variety, since there are so many and they're so commonly used in everyday speech.
Puerto Rican Spanish is a typical dialect of Caribbean Spanish, of which I am a native speaker in its Colombian Caribbean variety; we in the Caribbean basin often, very, very often drop consonants or even syllables when speaking informally, so you'll hear us say "pa" instead of "para"(for) "na" instead of "nada"(nothing) and even more evidently in past participles of verbs (ado, ido endings), so comido(eaten) is pronounced comío, pagago(payed) is "pagao", creído(believed or arrogant) is creío, also verbs in their infinitive from will lose the final R, so comER-->comÉ, pagAR-->pagÁ, creER-->creÉ. There's also aspiration or dropping of final or consonant-preceeding S, morphing into a sound similar to the Latin American J or the English H:
- Pescar = pejcá
- Las cajas = Lajcaja(j)
R is pronounced as L when preceeding T or D, so verde = velde, carta = calta. Note this is a feature of "islander" Caribbean Spanish (Cuban, Puerto Rican, Dominican) not shared by "mainland" varieties (Colombian, Vanezuelan, Panamanian).
Hope this gives you an idea of the differences of the language.