The two cuatros do not share a single string between them. One is strung with ten steel strings in five doubled courses; the other with four nylon singles. Confusing the two is not a small mistake — nylon on an instrument built for steel is slack and lifeless, and steel on an instrument built for nylon will pull the top off it.
Steel, in courses
The Puerto Rican instrument uses steel sets sold for it, in five pairs. As with any doubled course, change the pair rather than the string: a fresh string beside a worn one is brighter and louder and drifts away from its partner within a day, which makes a course sound broken rather than merely old. Keep the set you used written down, because the balance between the courses is what you are actually choosing.
Nylon, single
The Venezuelan instrument uses four nylon strings, and the fourth is the one that surprises people: this instrument's tuning is re-entrant, so the strings do not simply run low to high. That changes which string is under most tension and which one you will replace most, and it is worth knowing before you decide a set is wrong.
Nylon stretches. A fresh set drifts audibly for two or three days and then settles; tune often during that period and judge the sound afterwards rather than during.
How each one dies
Steel goes dull, gradually, until the figures on the golpe pages stop cutting — no break, just a slow loss of attack. Nylon goes false: it stops playing in tune with itself along the neck, so chords that were fine start sounding sour above the fifth fret while the open strings are still correct. Different symptoms, same fix.
One thing never to do
Do not string one instrument with the other's strings, and be careful with sets sold generically as "cuatro strings" by sellers who stock both. Check the count and the material before the label: ten steel or four nylon, and nothing in between.