It says a lot that in a thread about if 2 bands are in the same league there are a ton of people making generalizations about why they think one is the best (and it seems to be more Zep fans from what I've seen)
Seems pretty clear it's a regional thing for one, if you grew up in the US chances are you heard way more Zep but that doesn't necessarily make them better just because they're the band you grew up with.
Both bands put out plenty of great music, both bands were huge enough they were playing the biggest venues/festivals around. Both bands are still relevant with big followings decades later. That is the same League by most definitions. If you only are familiar with best tunes from one group you're missing out. Though I'd wager more people have heard all the Zep's hits before judging them vs Deep Purple, seems a lot of the people saying Zep are the best can't even name more then a few D.P. songs.
I think it's weird how much of a cult like following Zep has after decades, they still get defensive when you even try and say another band is in the same league if this thread is any indication. In the end some of these new musicians/bands smoke them both anyways: