Aegina's a better experience anyway -- because Hydra ferries are enclosed hydrofoils with salt-glazed windows, no view .. whereas for Aegina you also have a choice of conventional ferry (just 1 hour ride), where you can sit out on open deck & enjoy the seascape -- huge freighters & cruise ships, sleek speedboats, 3-masted schooners, on a fair day, even tiny sloops. Here's a great photo-sequence of a JUne daytrip - http://www.flickr.com/photos/36264706@N03/sets/72157621604646139/detail/ -- which shows some of t he highlights of the island.
Hydra brags about having no cars, but this also has the disadvantage of limiting how one gets around... riding a donkey? Climbing endless steps & lanes while jet-lagged? Not so fun. Aegina has busses (fewer, off season) cars & taxis, but I can testify that off season (even in late May during week, when I went) traffic is very minor)... I walked down a road for 15 minutes an no car went by. One can rent a car, but lately I hear that you now can also rent E-bikes, which are safe, reliable pedal-bikes with motor-assist... which means u can pedal if you wish, or just use the assist, and put-put sedately & safely along.
In April, I'd advise finding a nice hotel in the port town since the beach areas while great to visit, & stroll the sands, will just be "waking up" for the season, and likely won't yet have many tavernas & cafes open, unlike the port. PLus, the back streets of the town are fascinating, not touristy.. I love browsing in groceries & housewares stores just used by locals, seeing different brands, foods, decor items. HYdra is more for celebritiies, and for their fan clubs, where Aegina is the fun getaway for Athenians (and for some, the suburb, many residents commute daily for work)O.