I had to register so I could correct littlemo about the Passion Play. It is most definitely open and you can go online right now and buy tickets for performances.
Branson and ES are two wildly different cities. I don't care for the tourist trap, crowds, chain restaurants, etc. of Branson. But we go there with the grandkids because they can do the amusement parks, mini golf, go karts, etc. They do enjoy ES too but most of them like the constant entertainment of Branson. The older girls like Eureka better. In Branson I prefer Branson View Campgrounds out of the way but the kids want to be in the middle of town so it's Musicland.
Eureka Springs typically attracts a higher class of guests. They have much better dining options, unique and different. I can only think of 2-3 chain restaurants and they're fast food we avoid. More art galleries than t-shirt and trinket stores. It's a MUCH more relaxing and laid back atmosphere and just unique from any place we've been (except Europe--it has a European feel). Stroll around, take your time, tour. Lots of interesting history, nature, beauty. There's a lot to do, I can't fathom a day trip to see it all. eurekasprings.org is their web site.
We have stayed at Wanderlust & Kettle at the edge of town. Again I prefer to be out at Beaver Lake or even Lake Leatherwood but if we don't tow a car we need to be at the 2 in town to get on the trolleys/transit system to get around.
If you have any interest in trout fishing, check out Roaring River State Park too.