Rigid plastic liners are limited to their shape, so if you are wanting to create a more natural shape go with the EPDM. To me, EPDM liners are better because you can create your own shape and size and I feel you can more easily create a seamless transition between the landscape around them and the pond itself. As long as you keep them clean and filled they should last a good while. Plus, you can add plants and/or small trees around the pond to cast some shade. If you are going to have fish in it, this will also help keep them alive and happy because they too love shady spots. If the pond is low on water and the bare liner is left exposed it definitely can deteriorate much quicker, so keep it filled. EPDM liners are also easier to repair if the get a tear in them.
That being said, rigid plastic liners to have their place and advantages. Use whatever will work best in your situation.
I made mine with ferrous cement. The skimmer and waterfalls pond is a plastic liner, the stream is a liner. All have lasted 15 years now with no leaks. As long as you install them correctly you will have no problems. This pond is very large 15,000 gallons and has about 45 koi.