Is there any reason you are considering the S II LTE instead of the S III? Don't get me wrong, I love my S II LTE and I don't intend to upgrade to an S III, but as a new buyer why not go for the new technology?
I can't speak for the Exchange support, but when you use Gmail the app never needs to be manually updated. When messages arrive at your Gmail address your phone gets them instantly and alerts you. Many Android phones don't have alert lights, but the new S III does.
Rooting a device means that you (as a user) are granted full unrestricted access rights to the O/S. Through an app called SuperUser you can selectively grant this access to various apps. This allows you to install apps that would otherwise be unable to do what they do without being granted super user status.
I've tested the HTC One X and the Galaxy S III (and as I noted earlier I own an S II LTE). They all have approximately equal RF performance.
On phones OTHER THAN the Nexus line from Google, updates are handled through your carrier. However, if you root your phone you can install any custom ROM you like at any time. Using a Nandroid Backup you can take a snapshot of your phone's O/S, apps, and data and restore your phone to a previous state should you not like any of the ROMS you install.
Both the HTC One X and the Samsung Galaxy S III have "international" and "North American" versions. In both cases they provide LTE on the North American versions, but they go with the Qualcomm Snapdragon S4 dual-core processor. Their international versions do not support LTE, but come with quad-core processors. The jury is still out on whether the quad-core processors are actually superior to the Snapdragon S4.
You can read my full reviews of these phones at:
http://www.arcx.com/sites/Samsung Galaxy S III.htm
http://www.arcx.com/sites/HTC One X LTE.htm
http://www.arcx.com/sites/Samsung Galaxy S II LTE.htm
Note that the S II LTE HD is the same phone as the S II LTE, but with a higher-resolution screen. However, that screen is still powered by the same Adreno 220 GPU and graphics performance on the HD model suffers as a result.