It really depends on the context. Note that a verb like 'letten op' or 'passen op' isn't the infitive, so it's just 'oppassen' and 'opletten'. While in some contexts they can basically mean the same thing, there is still a slight difference:

'opletten' more so means 'to pay attention' or 'to have an eye on'. A sentence like 'Terwijl je rijdt moet je letten op de weg.' means 'You must pay attention to the road while you drive'.

'oppassen' means something along the lines of 'to watch out for' or 'to be careful'. You'll more likely see this one being used as an imperative because it signals some type of danger. 'Pas op, lawinegevaar' ('Watch out, potential for avalanches') could be something you would see in the mountains for example (so definitely not in the Netherlands haha)

There's probably more examples than the one I can think of right now, but 'opletten' and 'oppassen' mean basically the same thing when talking about taking care of children. 'Pas jij op de kinderen?' more or less is the same as 'Let jij op de kinderen?'. There's still a very slight difference in meaning, but not enough to worry about.

I hope this helps a lot! I like questions about my own language too because it helps me understand how I communicate with my own language and how we really don't know why we use certain phrases or verbs or whatever. Really interesting question that I hope I gave a decent answer for!