Does this put a lot of wear and tear on the back? More than sit-ups? Less?
Mjollner, you have to put your hands underneath your butt, palms down. Otherwise the strain on your lower back is too great and you can injure yourself.
One of the stretching exercises I do consists of lying on my back and lifting my legs perpendicular to the ground, holding that for about a minute, and then cross my legs over each other for about a minute, and then go into the Plow (yoga) position; i.e., let my legs drop down towards my head (with the legs straight, but soft knees), hold that for a while, and then bend my knees and with my arms push my lower legs on the ground. This stretches a lot of leg, buttocks, and hip muscles, particularly the piriformis.
That does not bother my back. If you have a bad back, it obviously is contraindicated. It will not aggravate any back problems that are non-existent. Perhaps some one will chime in and disagree, but I’ve been doing that for years.
Making a concerted effort to keep your lumbar spine flat against the floor throughout the whole motion should reduce the strain on your back. Putting your hands in the missbunny position (wink, wink) should facilitate this.
I’ve found something similar that is a good alternative to situps: you put your hands under your rear, so it’s resting atop them, then hold your legs out at like a 70 degree angle. Then you use your hips to bring them up; not your legs. If you really concentrate on just using your hips, you get a great ab workout. I do my regular situps special anyway, so I’m not sure how bad convential situps are, but I’d guess this is better for your back.
I used to (and still do at times) have horrible back pain in the lumbar region, which was apparantly caused buy a tight hamstring. I was incapable of lifting my legs in the manner you described. (One at a time, anyway. Both together was no problem.)Guess what one of my prescribed exercises was? Lying on my back (arms at my side–sorry missbunny) with my back as flat as I could make it and lift each leg as close to 90 degrees as I could. If I still did it, I’d probably never have back pain. 
I do it on my stomach. Raise my legs 90 from there to test to see if the lower back is acting right
When I had back trouble, my physical therapist had me do those as a hamstring stretch. The critical difference, though, is that you START with bent legs, and raise one leg at a time to a straight 90 degrees, or as close as you can get.