Firstly, a minor point: Wayne's dominant era is already a decade ago, and he is of the older generation of rappers now.
Wayne is not a "deep" rapper most times (although he has his moments, e.g. Tie My Hands and I Feel Like Dying). He's a punchline rapper - one who isn't trying to convey Meaning but just have fun on a beat. This tradition has a long history in hip-hop, going all the way back to the Sugarhill Gang and "Rapper's Delight".
His mixtape work is widely acclaimed as classic stuff - Da Drought 3, Dedication 2 and No Ceilings being the most prominent. His music has endless quotables, e.g. "real G's move in silence like lasagna"[0]. Rap heavyweights like Ice Cube, Eminem, Busta Rhymes, Kendrick Lamar, Nas and Raekwon have high opinions of his work, with hip-hop pioneer KRS-One calling him the "greatest rapper of all time[1]." Post-Wayne rappers betray a huge influence, with e.g. Kendrick Lamar, Young Thug, A$AP Rocky, and most prominently Drake.