I've been doing drainage/ basement waterproofing work for 28 years, and only used pvc the first year I have not bought a stick of perf pvc since, the only thing they are good for would be a septic leach field.
We do use solid pvc often, for carrying storm water but not for collecting it.
If you use enough stone either pipe would be ok, even no pipe.
The more stone below the pipe the better, it provides a greater buffer from sediment buid up.
In the real world, as a contractor we are trying to do the quickest, most cost effective job, for us HDPE is the way to go.
Single Wall – ADS Pipe
I've explained this before on other threads, with perf pvc, once the pipe is 1/3 full of sediment it stops allowing water in thru the holes, that's for the typical pvc with 2 rows of holes on the bottom. with ADS the pipe can be over 90% full and still take in water, because the slots go all around.
I've pulled out plenty of pvc due to this problem, no need to replace ADS until it's completely clogged.
We have never put a filter sock directly on a pipe, but we always use filter fabric lining or over a stone filled trench drain, as conditions may require. I have pulled out perfectly clean drainage pipes both pvc and hdpe due to clogged filter sock. It's relatively easy to clean a drain pipe on the inside, there's no way to clean the outside of the pipe.
What are you referring to when you say "french" drain? It means different things to different people, I know it's a common term, I just don't know how the french got credited with it
JB.