I know Jay would still be super relevant but let's not downplay Kanye here.
Kanye started this stadium status ish in hip-hop and Jay-z ran with that sound.
Throughout Jay's career he's looked at the leading man in the game and took his style to a certain extent. Started rapping slower like Nas and em. Got on that Mafiso ish like Wu and them. Was super-rugged and rapping on Swizz Beats' when DMX was popping. He set the pace in the game for the next few years. Came back.. tried to find position.... rode a movie for an album but that didn't capture the hip-hop community like that.. around the same time 'Ye sells a million first week with Graduation and Jay has basically wanted a slice of that type of hipster/mainstream/stadium rap since. Kanye has started to lose momentum and then he jumps on the JT a million in the first week wave.
Jay staying relevant? He'll always manage that. He can do anything, any style, pretty well. He'll be around. But the style he chooses to do it in, is dependent on who he riding.
He still biting 'Ye to a degree. Ye has always said how important art is too him. Fashion, architecture, artists, general cool things if anyone remembers his blog. 6 years later Jay-Z makes songs called Picasso Baby and Tom Ford.
Hov is still just about the GOAT for me but he certainly loves the attention.