Can't see how the weak society would last long. If a slave revolt doesn't bring it down (because it is a weak society, the military strength is therefore pathetic), then the petty and self-interested politics would eventually undermine its stability and it would collapse under its own weight. Depending on whats done, it could collapse in less than a decade.
A strong society could last as long for quite some time actually. There is literally a type of government based on this, ironically called the "Strongman government." The strengths of it are, usually, the leader has both the biggest dick and a rather charismatic personality that inspires either fear or adoration, or both. The weaknesses are of course, once the "strongman" dies, it either collapses in the ensuing civil war to replace said "strongman", or in the case of no suitable replacement, it splinters into numerous small factions. Though, optimistically, if a suitable replacement is found, then it continues until this guy himself dies. Rinse and repeat.
Personally, I'd expect the strong society to collapse quicker, but I'd expect the weak society's collapse to be a whole lot more brutal and bloody just because of the vindictiveness and desperation of weak-minded people.
So to me, this question could be simplified to, "Reoccuring, violent but brief collapse" or "Slow, but ultimately devastating oh-my-god-theres-blood-everywhere-look-at-what-they-did-to-Kenny-holy-shit-theres-guts-everywhere-imma-puke kind of collapse"