I go to both quite often. The Lodge by Yosemite Falls is lovely. If you do stay there, ask them (call them) and request the eco room. It is decorated in light colors and is really nice. I stayed there last year. Your other options are the tent cabins in Curry Village. They are pretty basic with an elevated wooden floor, spring beds, army blankets, electricity (not a lot). However, you need to use a central bathroom. I have stayed in the tent cabins, and even took my cousins from Spain there, and we were fine with them. I do prefer Housekeeping because it is more like camping, even though you sleep in beds. Although we take our own sleeping bags you can ask if they provide bedding. What I like about Housekeeping is that you can cook your own food, if you want, you have a little semi-private patio with a table, and you can have a campfire. It is also next to the river. There is also electricity at Housekeeping.
For Sequoia, if you stay in the cabins at Grants Grove, you might want to stay in a "regular" cabin as opposed to a rustic cabin. I stayed in a rustic cabin once, and the only light was provided by a kerosene lamp. It sounds really cool, but not practical if you'd like to read in the cabin, etc.
For Yosemite, I would recommend 2 nights, and definitely visiting Glacier Point/Washburn Point for magnificent views of the valley. If you like to hike, hike to Vernal Falls. If you like to walk, then a nice easy hike would be from the base of Yosemite Falls to Yosemite Village or Awahnee Hotel. You can also rent bikes there. They have a wonderful visitors center, worth exploring, and the rangers there can recommend many hikes that you would enjoy.
In Sequoia, I highly recommend visiting Hume Lake. There is a beach there and you can have a nice picnic. There is also a Christian camp, and you can gas up there, as well as rent kayaks for a nominal fee (I think $5/hour). It's fun to spend an hour kayaking on the lake. I also recommend Crescent Meadow, and taking the hikes/walks along there to Tharpes Log. It's just beautiful. You have to see the General Sherman Tree (largest living thing on earth), and climb up to Moro Rock, if you wish.
At Sequoia they have a campground with a stream running through it - Lodgepole. There is a trailhead to a 1.7 hike to Tokopah Falls. I really like this hike, not for the falls, but for the changing scenery as you go up.
I have links in my signature to a couple of trips I made to Yosemite and Sequoia, if you'd like to check them out.