Trenching for Downspouts

Where I live we have a high water table and a significant problem with water absorption in the soil. Sump pumps are the norm and run every 90 seconds or so to keep water out of the basement - I have two with battery backup to prevent flooding in the event of a power outage.
I am considering installing underground drainage tube to take the downspout runoff and route it to a section of the lawn where it can drain away normally. I intended to use rigid PVC pipe but have heard that professional installers use the flexible pipe. My concern is that the flexible pipe is not smooth on the inside and had a potential for settling and creating low spots. I suspected that I could direct bury the rigid PVC but would have to encase the flexible in gravel. Anyone done this or had it done? Thoughts?
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