There is a huge difference between these 2 types of back up and each is used for a different purpose. It is EXTREMELY IMPORTANT that you do both but most important of all you need to do the nandroid backup!!!
A nandroid back up backs up your entire phone, and by entire i mean every square detail!!! It backs up everything to the sd card and is your LIFESAVER if anything ever goes wrong when flashing a new rom or tweaking your rooted evo in any way. With having superuser status on a rooted evo it gives you the ability to break things or install incorrect things that will cause your device to have major issues that could be very well unfixable after you have done them. your should make a nadroid backup before you flash any rom or make any kind of non-normal changes to your phone. If you do this and things mess up you can the just reload your nandroid back up and restore your phone to a working condition before you or some program messed it up. IT IS YOUR LIFESAVER
On the other hand thats all it is good for really. it only does a complete system restore. If you do a nandroid back up and then flash a custom rom you will not be able to access any of the information in the nandroid to restore into the new rom. It only does a complete restore and thats it.
Titanium back up is the exact opposite as it backs system information up in a way that it is accessible after you have put on a custom rom. your can restore apps and there data as well as anything else you like that is compatible with the new rom. On the other hand, if things get screwed up, it will be of almost no value to you to fix what has happened, without having the nandroid you are screwed.
Personally i make a nandroid before every flash, i keep my very first and most recent nandroids on my phone at all times, but i also have every single one i have ever made on my computer in case my micro SD decides to crap out on me. also before i do anything i make sure my apps are updated in the market and then use titanium backup to back up all of my apps and app data. lastly I use my back up pro to back up anything else i want saved.... i do not however back up my contacts or calender as i have all that info on google and there is no reason to. after i flash a rom i download titanium from the market and then restore the rest of my apps, sign into google and get all that info restored, and then use by back up pro to restore anything else.
needless to say, i felt it was important to explain the difference and i hope you get to read it before you go to far!!!
best of luck and hit thanks if this helped