I own and have used both a lot. The Asics Pir is my favorite road racing flat. I bought 3 extra pairs after my first once because I knew that asics would change the model and probably mess it up.
As for width, I'd say they are pretty similar.
In terms of which is more shoe, they are very different. The asics is much more shoe and is a great road flat for anything from 5k to half marathon (I wore it in a half and it was a great shoe for that distance). It is very light, but if you have clean form and aren't super heavy you can definitely get away with wearing this shoe as long as a half, maybe even longer.
The wave universe is very, very light - the lightest shoe I've ever run in. It is the closest shoe I have ever found to feeling barefoot. It is thin enough that you really feel any little rock or pothole. I would not recommend this shoe for anything longer than 5-8km. Unless you have a lot of experience running barefoot, this shoe is probably too minimalistic.
So, I would say go with the asics. This is really one of my favorite shoes. It is very light, but still gives enough support to feel like you are wearing a shoe, even for 13M+.