Personal choice really. I've never used a range extender but my daughter has in her 1960s house and found it worked OK - one of her sons had problems connecting his laptop in his bedroom.
I use powerline adapters, mainly because I like to have my desktop computer connected via ethernet, rather than wirelessly. The router is in the hall and can't be moved; the desktop is in our third bedroom.
With the extenders you simply plug them in and the wifi range is extended. With powerline you connect the router to the adapter with an ethernet cable, position the other adapter near the computer and connect it via a second ethernet cable (cables usually supplied with the adapter). You then "pair" the adapters (easy instructions supplied) and away you go. If you are short of mains sockets you can get adapters with mains pass-through, so they don't take up a mains outlet.
You can add extra adapters to the system if you wish; all makes will pair, so you don't need to stick to one brand; I have two different makes as I have my internet radio connected via ethernet cable as well as my computer and the router.