Here's a side-by-side of old vs new. You can see that they removed a lot of the detail from the old logo, which makes for cleaner lines and better rendering on screens... But at the expense of quite a bit of character.

The regrettable thing about this logo is that it, like the stretch Y that we all love, was a pretty generic copy-paste logo back in the day. There were dozens (DOZENS!!!) of teams that had secondary logos featuring cartoonish mascots with freshman caps. Similarly, the "Stretch Y" or oval Y helmet logos were generic decals that anyone could order out of a sports-supply magazine; they have an entire alphabet of decals in that style, and a number of college teams used them back in the day. Even now, you can still find decals for sale in that same font; for example, here is an R and here is a K.

With that in mind, I don't get too keyed up about BYU logos anymore. The ones in heavy use today were generic template-type logos when introduced so I don't feel like they're sacred. I'm also not too keen for a rebrand - Nike rebrands don't age particularly well (look at what they did to Utah State, for example... Or even to BYU back in the early 2000s!). That said, BYU does have a truly unique logo, which is my all-time favorite. I wish they'd use it more.