The beaches on both coasts are great. The difference is that the East Coast has the Atlantic Ocean and the West Coast (St Pete, Clearwater, etc) is the Gulf of Mexico. So on the Atlantic side, you have real waves -- in fact, many of the beaches are popular surfing venues. On the Gulf, you've got a more tranquil, often waveless, setting.
We were just there last week on a non-park trip and went to both coasts.
The other difference -- which matters for a day trip -- is driving time.
The closest Atlantic Beach (Cape Canaveral & Cocoa Beach) is about a one-hour drive from WDW, expressway the entire way.
On the Gulf side, we went to St Pete Beach which was about 2 hours, complicated by major construction just west of downtown Tampa, but also expressway virtually the entire way. Beaches in Northern Pinellas County (Redington and others) would be a little less drive time -- maybe 15 minutes less. Clearwater would be about 2 hours or maybe a little more because it's more north.
We actually went to St Pete Beach first, then Cocoa Beach, and finally Daytona, New Smyrna and Canaveral National Seashore. Daytona (especially Daytona), Cocoa Beach, and St Pete Beach are very touristy. Nice, with lots to do, but touristy. New Smyrna is much less crowded, much more laid back.
Canaveral National Seashore is a ghost town. If you want to see Florida beaches like they used to be, go to Canaveral National Seashore! If you want a day in utter tranquility...go to Canaveral National Seashore. For more info,
www.nps.gov/cana
Full disclosure/Fair Warning: This seashore is a National Park Service site. Don't expect all the creature comforts or elegant restrooms!
The facilities are more, um..."environmentally friendly" (or maybe not really, but at least waterless).