Do curved stair-lifts work the same as straight ones?

The simple answer to this would be yes, they do. Straight and curved stair lifts work on the same principles and it is only the frames and the rails which are changed in order to accommodate the different shape of stairs which is being worked with.  Curved stair lifts may well move slightly slower in places as they have to maneuver themselves around bends safely and smoothly but this is likely the only difference which you are likely to find; you still get into the chair, control its movements and exit it in exactly the same way as you would with a normal straight stair lift.  

Getting a curved stair lift or a straight one is a decision which is always going to be dictated to you by the structure of your house and thus it is not something which you should lose too much sleep over; they both work in the same way, they are just aesthetically different and a couple of slight changes have to be made to accommodate the curving framework- you should spend more time worrying about what sort of stair lift you want.

Stair Lift Information Guide: