Delrin-
Pros- Stable, self lubricating,consistent diameter, very strong material.
Cons- Tricky to glue, some makers will tap and thread the tenon/mortis and also glue to eliminate risk of the tenon pulling out of the stem,limted choice of colors, the space required for the tenon fitting inside the stem can limit design choices.
Hand turned-
Pros- made of the same material as the stem, no chance of it pulling out. You can adjust the tenon diameter slightly to vary the snugness of the tenon mortise fit. I also think it looks better.
Cons- not as strong as Delrin.
Some of the top guys in the country do use the Delrin tenons because they think it does a better job...Either method can produce good tenons...
I prefer to hand turn tenons except in the case of bamboo which requires skinny tenons (most guys use stainless tubing for that- I get a larger ID with carbon fiber tubing, and the epoxy base used in the carbon fiber glues very well)