Epcot or Hollywood Studios

IIRC a lot of Hollywood studios is under work...

Hollywood studios has some good attractions for kids such as toy story midway mania, voyage of the little mermaid, disney junior, Beaty and the beast live, muppets vision 3D and star tours. Then there is fantasmic and Star Wars spectacular for night time shows.
On the other hand epcot has some great rides for kids like the whole seas pavilion with finding nemo, soarin and the land pavilion, journey into imagination with figment and there will be the new frozen ride in the Norway pavilion when you go. only has illuminations firework show at night but world showcase is really nice at night.
In terms of more thrill rides, hollywood studios has rock and roller coaster and tower of terror but may be a quite intense for kids. Where as epcot has test track which is less intense for kids.

If it was up to me I would chose Epcot because it is more of a whole day park where as with the studios can be done in half a day.

Epcot because you'll get more bang for your buck. You can spend a whole day easily in Epcot but it's hard to do that in Studios since there isn't a ton to do.

You could do both. They are very close to each other.

I would give a slight edge to DHS just because of the ages, but EPCOT has a lot of hidden gems.

Although much of DHS is under construction right now, I'd still recommend it over Epcot simply because it has more rides and nighttime shows. Now if you were going with older children like around their late teens, then I would recommend Epcot since it's just a cooler experience overall. But since your going with younger children, I'd recommend sticking with DHS. Just make sure to see Fantasmic!

So I'd say it really depends on your kids specifically. EPCOT Can be more intellectual, and a little more real world. But some kids will love the experience of walking through the countries, and the SEAS pavilion. Hollywood Studios, on the other hand, is really about the characters. You've got Little Mermaid, Beauty and the Beast, and Toy Story. So if that's what you think your kids will be more into, do DHS. If you think they'd be more into experiencing other cultures, and seeing cool shows from them, and seeing the fish and a fun loving purple dragon they've never seen before, I'd do EPCOT. I know that as a kid, I liked EPCOT a much more. I don't know your kids. I can't even pretend to. So Id just think about your kids and what they'd enjoy more.

How about Lego Land... Great for little ones...