Elastic, because they are around a horse's shoulder, there will be a lot of movement. It'd be like wearing a stiff ankle brace, it doesn't give at all, but when you put an elastic brace on, you have more freedom.
The whole point of them is to keep the saddle from slipping back, so you don't want them to have a whole lot of give.
Also, if you have ever seen an elastic breastplate snap it can be a disaster. I would never put one on my horse.