What exactly does the Mountain Lion Migration Assistant transfer?
Apple has a very nice explanation of how Migration Assistant works, what steps and accessories you need and much more:


How to use Migration Assistant to transfer files from another Mac


In a nutshell, Migration Assistant has three bins of data to move:


Applications (just the programs - no user data or settings transfer)
Users (the user data, settings, preferences, saved files and such - but no Applications. You could have all your Word docs, but no Word to edit them in this case)
Everything else that's not an App or a User. This gets oddball things like /Users/Shared files and folders that don't belong to one user, unix and command line tools like homebrew that get installed outside /Applications and /Users. 


So with three check marks (let's assume you don't have multiple users), there are 7 combinations you could migrate - each leaving a different set of data on the destination Mac. (If Applications was A, Users was B, and Everything else C) You could combine them as follows: A, B, C, A+B, B+C, A+C, or A+B+C

I would say, you get to experiment when you get your new Mac. Run the migration you think is best, and then test it. If you don't like it, erase the destination Mac (booting into recovery mode, erasing the HD and re-install a clean OS might take 25 minutes on a fast network - the OS download is 4 Gb or so) and re-run the assistant.

For me, I would recommend both migrating from your Backup and then optionally re-migrating from the old Mac. It's important to test your backup - when was the last time you tested a restore to be sure you have a viable backup?

Everyone says "make sure you back up" but they really mean and might be better saying is, "make sure you can restore your backup and it has what you need!"

I would encourage you to configure your Time Machine on the old Mac to exclude any things you don't want moved to the new Mac, make a back up and write down the time of the back up. Then eject the backup drive and change the backup settings to back everything up again.

You could take that "latest" backup and Migrate it to the new Mac and test for a while (re-connecting the backup drive to the old Mac) to keep your "main" Mac backing up. 

As you test the new mac for a day or so, you can decide it's time to move over. At that point, turn off Time Machine on the old Mac and connect the backup drive to the new Mac. It will offer to "inherit" the old backups and you can move forward. Worst case, you still have the backups to restore something needed and then can clear the old Mac for donation, sale or mothballing.