Experimental date indicates tert-butyl cation is more stable. Specifically, the benzylic cation releases more energy when combined with hydride, indicating that it is less stable. This is called "hydride affinity", a term you could google. This seems to go against the rule of thumb that ions with conjugation are more stable than ions only stabilized by hyperconjugation.
https://en.wikipedia.org/wiki/Carbocation <--This link talk a bit about hydride affinity.
I recall reading somewhere that some experimental results can seem inconsistent with hydride affinity. But generally this is what people refer to first when assessing carbocation stability.