They both mean always/at all times, palagi is just lagi with the pa- prefix, in this situation the pa- prefix doesn't really do anything. I can't explain in words what pa- does, but I got a feel for it by looking at examples:
baba = root word of down
pababa = downward; downhill
lapit = root word of closness
palapit = oncoming; approaching; toward; coming closer
taas = root word of height
pataas = upwards; upward; heading higher; heading up; increasing; escalating
balik = root word of returning
pabalik = in return; on the way back; backward
uwi = root word of going home
pauwi = on the way home; starting to go home
takbo = root word of run
patakbo = running; while running
labas = root word of out
palabas = coming out; headed out; outward
All definitions here and more can be found on the dictionary of this website.