My parents ate a kosher turkey and believe it is the most delicious turkey they ever tasted. They asked me to find out about it.
My guess is that the kosher turkey is salted, and the salt is why it was so delicious to them. They follow a low-salt diet.
Or maybe kosher turkeys are fed a "proper diet" that gives them a better flavor?
Should I try to buy a kosher turkey for Thanksgiving, or can I kosher it with salt myself at home for them?
I don't know about the particular origin (who raised it) of the turkey they ate. Often the poultry come from several major farms, and the difference comes from the slaughtering and handling of it.
Kosher poultry are slaughtered by kosher slaughterers (shochet in Hebrew). The shochet performs the act of slaughtering the animal with both religious intent and attention to the physical rules designed to minimize the animal's suffering and hasten the animal's bleeding out period as much as possible. This same principle applies to the slaughtering of animals for meat.
Next the poultry is "flicked" - the feathers are removed with cold water only (not hot) - and then it is soaked in cold water. After its innards are removed, it is soaked again. Then it is salted externally and internally. The purpose of these three steps is to remove all possible blood.
I do believe you are correct that the residual saltiness made the kosher turkey more tasty. The salt used is similar to the amount that some people use in "brining" a chicken or turkey in the cooking of such birds. In taste tests, kosher birds have done very well.
Should you buy a kosher turkey? Sure. Should you purchase a regular turkey and brine it? This might make your turkey more tasty than in the past, but the turkey would not be considered kosher for any Jewish guests who observe the Jewish Dietary Laws of kashrut.