Is it better for me to forget about Fragments and continue to develop with TabActivities?
IMHO, no.
Get a copy of ActionBarSherlock and add tabs to the action bar. This is a tab template going forward with Honeycomb and Ice Cream Sandwich, and ActionBarSherlock allows you to use the same approach for Android 2.x devices. You should serve in the future rather than in the past.
Note that you do not have to use tabbed snippets for the action bar, although you can.