According to this thread on Android Forums:
http://androidforums.com/htc-rezound/676666-handcent-mms-problem.html
there are two things that others have found to get Handcent to send MMS.
1. In handcent go to settings...application settings......default messaging application..... Then pick at the bottom "use for all SMS & mms"
...
2. have to turn on 4G or the MMS never goes through.
I assume "turning on 4G" means Mobile Data. Evidently the stock text app will turn on mobile data and send if it is off, but Handcent will not. Once the stock text app turns on 4G/Mobile Data then both send. That's my 2 cents.
A test is to turn off WiFi and turn on Mobile Data and try to send from Handcent. Does it work?