Help me choose between LiveView and Vue

I think it really depends on what the requirements of your project are.

if you only need some custom form elements or validations, etc. then LiveView requires a lot less boilerplate than Vue to do the same things.

However if you want to build a Single-Page-Application, require interactions with complex JS APIs like the canvas, video or audio elements, or need pages to keep on working if the user goes offline, then this falls outside of the feature set that LiveView provides.