Is it true that allylic free radical is more stable than allylic carbocation?
This is trickier than it sounds because you have to compare things that are similar or maybe you won't get the comparison you want.

First, you can't compare the energies of two things that don't at least have the same components. In this case, the allylic radical has an extra electron over the allylic cation. Let's say you generated the radical by fragmenting propene via removing a hydrogen atom or a hydride anion, respectively, as the other product. Notice that you there is energy in the other product, and you can't really just compare the radical and cation without taking into account the other product.

Second, you're in a situation where you make one species from the other. In fact, if you ionize the allylic radical, you will make an allylic cation. Notice that since you are ionizing a neutral species, the ionization energy is positive: you're going to need to add energy into the system to remove the electron. This makes sense because that electron is stabilized by the 8 nuclei that are present.

So, while you can't really compare the two species in your question head-to-head, it's clear than you can create the cation from the radical by adding energy to remove an electron. But this doesn't mean the cation is higher in energy; it just means the cation and the electron separated at infinite distance are higher in energy than the radical.

Hope this helps.