Well, priority is a complicated subject. There are many different phenomena in the game that we like to lump together as humans and call "priority". It's some conglomeration of:
- Size of hitbox, and disjoint of hitbox from hurtbox
- How fast the hitbox comes out / how fast it disjoints / how long it stays out
- Different types of hitboxes: regular vs. transcendant, and some subtle "elemental"-type effects (e.g. water beats fire)
- When and how some moves can "clash" against each other
In Brawl, only some moves were able to "clash" (i.e. the hitboxes hit each other and then one or both moves would be cancelled, returning the attacker(s) back to neutral). Most ground moves could clash, notable exception being MK's sword which was transcendent even on ground (yikes.. his only clashable move was dash attack... whyy sakurai). Most aerials could not clash, notable exception being Olimar's Pikmin which were treated as separate hurtbox characters.
Specifically interesting is that in Brawl, moves that could clash, would clash "even" and return both characters to neutral, if the hitboxes would deal within 5% damage of each other. This is after stale-move negation was taken into effect. If the difference was > 5%, then the stronger move would press on and only the weaker move would be cancelled.
Long story short, lots of different aspects of the game contribute to what "feels" like a concept of priority, and many people use that word differently. Espy considers range separate from priority. But most people talk about G&W having huge priority, and that's mostly about the disjointedness of his hitboxes (hitbox is far from hurtbox), and that those hitboxes tend to linger (though usually not as much as the animations may suggest). So that's kinda just range. In a different (perhaps more accurate?) sense of the word, Ike has huge ground priority because his attacks are so strong, they will win clashes vs. other weaker ground moves. But MK's priority is even better because his transcendent moves cut right through anything without clashing..... although that makes them unable to block some types of projectiles (e.g. din's fire) that other character's attacks can break by hitting it.