We are getting ready to begin redevelopment of a large aging internal enterprise application. We have decided to use ASP.NET MVC, but under consideration is which Object Rel
Short answer: use both (i do really use both)...
With ORM there are multiple possibilities, all depends what you want.
As a real ORM mapper I strongly recomment NHibernate and Fluent NH mappings. You need a lot of research to put together a nice architecture, but then nothing stands in your way. With minimal compromises you get real flexibility.
EF6x (core is not prod.-ready IMHO) is called an ORM, but what it generates is more closer to a DAL. There are some thing's you can't do effectively with EF6. Still, this is my favorite tool for a read-model, while I do combine it with NHibernate (where NH I use for a DDD/write model).
Now to performance - its always pro and cons. If you deep deeper into ORM architecture (see my article: avoid ORM bad habits) then you will find intuitively the ways to make it faster. Here's my another article on how to make EF6x 5x faster (at least for read situations): EF6.x 5x faster