I know 2 vets who love WWP. Made a huge difference in their lives.
There are lots of good charities.
There are 2 questions you should ask yourself about any charity: is it reputable and what kind of programs and services do they offer? WWP is large and offers a lot of different programs that deal with lots of issues vets have. The vets I know benefited from their mental health (ptsd) programs.
Check out the ones that others listed and learn how they help vets and pick the ones that provide the programs that matter most to you.