I love recharge dice.Actually that is not it, but that is a good guess given my history.
I like X/Rest because it is a narrative the makes sense to me. Needing to rest implies the ability takes something from you (stamina, magical energy, etc.) that you then need to recover in some manner (by resting). A Recharge is the same narrative idea in theory, but the randomness and undetermined nature of the method of the recovery undermines that narrative for me a bit.
To be clear, this is not a big deal to me, I use both and think they both have their place.
Also, there is a gamist reason. I don't want to roll a bunch of recharge dice!
Shocking, I know.