Nandroid backups are full system images of your device at the time the backup was made. They are not good for restoring apps to a new ROM. Nandroids are all an or nothing recovery tool.
To backup data between ROMS - Titanium (and there others on the market but I use Titanium so I'll use it as the example) is good for backing up data when moving from ROM to ROM. However, let's think about what really needs to be backed up...
e-mail - Gmail is saved on the Google Servers so no need to back that up. POP/IMAP Exchange email is also backed up on the mail server so again no need to back that up.
Contacts - Gmail contacts are automatically backed up to Google's servers. Phone contacts can be backed up using the export/import function in the contacts app.
Bookmarks - Titanium backs up bookmarks and this is one of the very few pieces of system data that can be restored on any phone.
Apps - What apps really need to be backed up? Apps that hold state or current progress information and that's it.
Apps like Angry Birds (as an example) store your progress locally and if you do not back it up you will lose your progress, so game data can be backed up and restored.
Bank apps? Nope - everything is on the bank's server. just re-download and login.
Weather Channel? Nope - the handfull of locations you can monitor can easily be re-inputed after a fresh install.
Beautiful Widgets? Nope - If you have the paid version, you can re-download from the market and re-set up your preferences. If you want to save the data so you don't have to re-download skins then this is another where you can restore the data after re-installing the app.
The big advantage to backing up all your apps with TI is that you have a list of what was installed. You are better off doing clean installs from the market for apps that do not hold state. Another way to manage which apps you had installed is to use AppBrain, it will sync what apps you have installed but AppBrain does not save data.
SMS - Now this one is a personal thing. I don't care if I lose my SMS. I don't hold every text message as if it were a precious illumination by DaVinci, however I know that some people do. There are apps in the market that will restore SMS messages, even when moving between ROM's but they are not a fix all. If problems develop after restoring, then you want to roll back that restore.
Other than that, what else needs to be restored from an old ROM? Any config?s or screen setups would have to done over again anyway. You would want to take advantage of any features the new ROM has so restoring old setups will do more harm than good.
So, after a very long-winded dissertation, Titanium is good for moving from ROM to ROM, you just need to be knowledgeable about what is safe to restore and what is not safe to restore.
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