Hi Ken,
I just did the upgrade from the 2.2 Assignments module to the regular Assignments module (the 2.3+ version). I THINK the difference between the two, and the reason I chose to upgrade, was that Moodle 2.7 does not support Assignments 2.2 module (and we are planning to upgrade to 2.7 soon). "Assignments" is not just a 2.3 version, it's for all Moodle versions after to 2.2, and these assignments are not automatically upgraded. That Assignment upgrade tool you are referring to is the means in which you can update them to the non-2.2 module.
I think it would be a mistake to used the Assignments upgrade tool WITHOUT telling your teachers. There may be lots of panicking!
My teachers only noticed a difference on the Assignment's grading page. They liked the 2.2 version better, and were SHOCKED to see it look different. There wont be any differences on how the actual student assignment LOOKS, but there are minor changes in the Assignment settings page, mostly with flexibility on # of files to upload and file size limits. Think of the new Assignments module as a combination of all three Assignment 2.2 options -- all the settings you need in once place versus having to decide which settings you want to use PRIOR to creating the assignment. I think that's the difference between the old 2.2 and the new Assignments activity.
DO prepare the teachers for the change--a teacher's main job with Moodle is to teach & grade. You will be changing the looks of 50% of what they do, and they will panic if they aren't given a proper heads up. Do train them on the difference between the two. My teachers are VERY used to the new Assignment's grading page now, but it was a shock at first since they were so used to using Assignments 2.2 for years.
Yes, as an Admin, you can remove the entire Assignments 2.2 in your plug in settings. There is no default assignments module, you have to choose one or the other (with the three options) so disabling it will prevent teachers from accidentally using the old 2.2 module when creating new assignments.
Good Luck!