Ok, I see what you mean. Alright, maybe I should have phrased this a bit differently. It's really hard to explain why 'odpocząć' is more likely in such a sentence.
So, technically 'medytacja pozwala mi odpoczywać' has two meanings:
1) Meditation enables me to enter a state in which can I rest.
2) I regularly use meditation in order to rest.
The problem with 1) is that it sounds a bit like it would otherwise be impossible to even begin resting. Furthermore, it says nothing about whether or not it is effective, whether you are getting the amount of rest you actually need.
The problem with 2) is that it lacks some more context, like (odpoczywać po pracy). Of course, the context could be implied, but since that's a rather specific scenario it's better to specify it, imho.
You can take a look at sample sentences in the Polish Corpus:
[base=pozwalać] [cas=dat]? "odpoczywać|odpocząć"
There are 18 examples for odpocząć, but only 3 for odpoczywać.