Generally speaking, Nandroid should be used to create a full system image of your existing setup. This backup includes /system /data /boot your caches and everything else. Doing a full restore of a Nandroid backup is like taking a time machine back to a previous snapshot in time. So this is very useful for going back to a previous point if something goes wrong with a new ROM. Titanium Backup should be used to backup all of your apps and data, which you can later restore to a new ROM in one big batch. TB has other functions, but this is the big one.
So to summarize, Nandoid for a full system image to restore for those "oh no" moments, and TB to restore your user apps and data.
Note on TB: It's rarely a good idea (if ever) to use TB to backup and/or restore SYSTEM APP data from a previous ROM. User apps you downloaded from the market are fine, but restoring system data is asking for trouble.
However, sometimes restoring ALL App data in TB can cause problems in a new ROM as well, for a variety of reasons. Not always, but issues can come up. So when I flash a new ROM, I usually only restore Apps that I absolutely need to keep the data for. For the rest, I use an application called Appbak. Appbak creates a text file out of all of your existing Applications and stores it on your sdcard. When you wipe your phone and flash a new ROM, you re-install Appbak from the market, run the restore function and select your text file. Then you can click through each App on the list and it will take you to that App on the market so you can download and install it.
You can also navigate to the Android Market on a computer, log in and click "My Library", and will list all apps you've purchased and many that were free that you simply downloaded. From there, you can push Apps to your phone.
SO ...
to answer your question. You basically have two options at this point to get all of your App data into your new ROM. Try this first ...
Boot into CWM, choose Backup and Restore > Advanced Restore > choose your backup file > then choose Restore Data. This MAY work for you, but it may cause problems as well, so ...
If the above doesn't work or causes problems, I would recommend you do a full restore of your previous Nandroid backup, backup all of your Apps with TB, then re-flash the ROM again. Then reinstall TB from the market and restore User Apps + Data.
Good luck!