Most people believe that chaise lounges are do-able and daybeds not so much, by default connecting daybeds and chaise lounges to luxurious comfort and relaxation with homes that can afford them, afford them as in financially and also spatially which is just another way of saying financially... I think a little imagination and thinking out of the box is in order here.
Because chaise lounges are smaller in size, suitable for one person only, it's easier to find a space for them if you're living in a limited space home, chaise lounges are even do-able in apartments and can really lend a comfortable & luxurious old world charm to the space.
Daybeds are generally bigger in size and can be set up outdoors or indoors but I think you'll be surprised how small daybeds can get (ie. a single bed). I find that outdoor daybeds are pretty popular amongst interior designers though if you don't have space outdoors (like me) you should really think about setting up a day bed indoors, this can look quite pleasing and is done pretty often by apartment dwellers. The easiest thing to do when setting up a daybed indoors would be to set up the daybed as a sofa in the living-room.