I never played one of the Epi Explorers, but I think its the thickness of the neck, and the 2 3/8" width at the body that gives the Ovation so much girth. The basses I usually play have pretty scrawny necks, though, so it might just be my own point of reference that makes me see it as huge.
It was a very innovative design, and also built like a tank! It gets plenty of great Ric-ish/Fender-ish/... sounds, but I think if it did one sound well that was really unique unto itself, I'd probably use it more. Still a fun bass to play, and they can still be seen in the US $5-600 range - not bad for a 30+ year old mahogany bass.