Aran Island or Connemara?

Neither.

Skip the boat. Instead, fly to Inis Mor (crazy cheap - flights are subsidized by the government). Take the first flight of the day outbound, the last flight of the day returning, that gets you more time on the island. It's cheap, fun, and super easy (they have a shuttle bus you take from downtown Galway to their little airport, and back - buy the bus ticket along with the flight ticket, unless you have a car). The plane ride is short (under 10 minutes, from engine start to off), utterly thrilling, perhaps terrifying for some (tiny plane, treetop altitude) scenic...and over all-too-soon. Ask nicely if you can sit in the copilot's seat - the views are incredible (just keep your hands and feet off the controls, don't touch anything in front of you, and don't bother the pilot once the engines start, he's busy flying the plane).

The cliffs on Inis Mor are 100X better than the more famous (and touristy) Cliffs of Moher.

That's a tough choice, in my opinion! But, I'd say do the boat excursion to Aran Islands if you only have one day. I enjoy taking the boat to Inishmoor over a plane as you are able to see all the islands from the sea instead of a quick flight over and, quite frankly, I enjoy a good boat ride. Keep in mind, in April the seas could be a bit rough so just be prepared and, as always, be prepared for all kinds of weather--it is Ireland afterall. While I think Cong is charming and Connemara stunning, I'm not a fan of Kylemore Abbey (one of the most disappointing sights I've seen in the whole of Ireland) which is the only reason I'd put this second. Hope you enjoy your visit to Ireland!

I can’t compare because we didn’t have the opportunity to experience both your options, but the boat ride to Inis Mor, the time we spent on the island, and the return trip with the up close views of the Cliffs of Moher was one of our favorite Ireland experiences last May!