It really depends on what you are looking for. Many people favourite side is the gulf because the sea is a lot warmer, the sand is white and generally because they've always gone that way to explore.
The Atlantic has its qualities too, if you are prepared to explore them. The sea is more fun,IMHO, with its larger waves and the sand is like most destinations in Europe.
Both sides are good and we've enjoyed excursions to Daytona, Ft. Lauderdale, Pompano, Miami, Melbourne, Vero just as much as we have Clearwater/ Indian Rocks area, Captiva, Marco, Sarasota, etc.
Why not do both ? You can be at Clearwater in 90 mins from the Disney area and about 70 minutes will get you to the other coast to explore Daytona/ Cocoa. Have the best of both worlds !