Linguistics

Portuguese is more conservative on analysis; like, the phonemic inventory doesn't change that much from Continental Proto-Romance. But once you look at the surface, you find a bunch of weird stuff, like:

• a general tendency to convert /Cl/ clusters into /Cɾ/; see praia/playa, cravo/clavo, or dialectally *prástico (standard: "plástico"). You typically don't see this much in Spanish, except in the Caribbean. It's nowadays stigmatised but still an ongoing process in some dialects (like Caipira).
• even conservative Portuguese dialects have a tendency to shift to stress timing on quick speech, with vowel reduction and/or elision. On the other hand Spanish typically keeps itself syllable timed, even on quick speech.
• most intervocalic /l/ and /n/ are gone, except in reborrowings. Some /n/'s got regenerated as /ɲ/, but that's from a nasal vowel splitting again into oral vowel + nasal consonant. See e.g. cor/color, coroa/corona, boa/buena.
• the nasal vowels are becoming phonemic, Lombard/French style; in some situations you can't simply analyse, say, [ẽ] or [ə̃] as /eN/ and /aN/ any more.
• rhotics. Unlike Spanish, Portuguese never backed /ʃ/ into [x], so there was that "gap" in the phonology that got filled by /r/ instead: [r]→[ʀ ʁ ɦ x χ h], with all intermediate links popping up in some dialect. In the meantime /ɾ/ became [ɾ ɹ ɻ], with [ɻ] trying to split into a third phoneme.

There's also a bunch of phenomena that appear in both, but got stigmatised in Portuguese and accepted in Spanish. A good example of that is yeísmo - it does pop up in Portuguese but it's associated with rural people, and seen as "poor speech".

Sorry for the wall of text.