which one do your prefer?airbed or plank bed？  

when you say plank bed what do you mean exactly? I have what we call a platform bed, I need no box spring just a good mattress. I like airbeds however and if it were not for fear of holes I would buy one to replace my mattress.

So your sister feels like sinking into 'dessert' when she 'laid' down on 'air bed'.

Is she doing Yoga exercises? Yoga people prefer the flat and hard plank bed.

we have all kind of beds over here not only those two. Also if you have a bed with planks on the bottom you have to look for the right matras. There are so many matrasses. All different made, different high. So the kind of bed is not important but the kind of matras you choose. Or you have to choose for a waterbed (bag filled with water) or air bed (filled with air).
BTW a matras you should turn over and over frequently and every 5 years you should buy a new one. I think that is way more expensive as an airbed. But.. you can put a normal matras on an airbed too. I read that has the same effect as an waterbed (just cheaper) and if you lay on a matras you don't sink into it (which I would like too).
You have to try out what fits you most and in what you will have the best nightrest.