Caveat: I owned the original Transformer (TF101) and currently own the Transformer Pad (TF301), not the Prime unit or Infinity. Difference between the units is mostly unit build elements and some speed. I also own a Nexus 7.
That said, I am able to compare the 7 inch Nexus 7 and Transformer tablets for you.
OS: Nexus 7 is running Jellybean now. Transformer will get it (Asus is very good about updating their hardware), but for now you get Ice Cream Sandwich. In future, the Nexus tablets will ALWAYS get the latest iteration of Android first. So if you are the type of user who has to play with Google's new toys now, you'll be happier with a Nexus.
Storage: The Transformer comes with more memory out of the gate (16GB or 32GB with microSD card slots. Nexus 7 gives you a choice of 8GB or 16GB and that's it. So if you are a digital hoarder (i.e. someone who needs to store video when away from an internet connection), you'll be happier with the Transformer.
Portability: The Nexus 7 is roughly the size of a paperback book. It fits inside a jacket pocket, purse or jeans back pocket. It's extremely light and easy to hold in one hand. The Transformer is a 10" screen that must be held with two hands and carried like a netbook. The Prime is also made of metal and glass (the TF301 has a plastic backing) which makes it heavier, as in iPad heavy.
Usability: The Nexus 7 is primarily meant to be a media consumption device. Watching video, playing music, reading books or web pages, playing a few games, these are all perfect on the 7 inch size tablet. You can write via a pop up keyboard, but it is very tiny and can easily cause hand cramp. The Transformer not only has a bigger netbook-sized screen, but can add a chicklet keyboard dock to make typing as fluid as a netbook. (The dock also gives you an SD card slot and USB port for mouse or USB HDD.)
Bottomline: If you want a tablet mostly to consume media, get the Nexus 7. If you expect to be doing more writing or content creation, get the Transformer.
Usually I take my Nexus 7 into the bathroom, or lying in bed, or in my purse for day trips. If I expect to do some writing and have access to a table/desk, I'll take out my Transformer. My Nexus 7 is my ebook reader while my Transformer is my Android netbook.