If you think about the concept of a Mach 3, you're getting three passes in one. What's more there are a lot of "training wheels" on a Mach 3 that you have to take responsibility for with a DE.

I use a vintage Gillette Slim and once it "clicked" I began getting better shaves in two passes than I could get from a Mach 3 in one or two passes. And IME the DE blades (regardless of type) last longer than the cartridges. My beard's not terribly thick; about average I think, but very very wiry and coarse.

Keep working at it and you'll find your shaves improve to surpass your prior experience with the cartridge.

Peace,
Jim