There are many advantages to handloading turkey ammo, primarily if you are loading TSS. If loading lead, there is no real advantage in either cost or performance vs factory ammo. You cannot load cheaper than Winch gray box or Fed Turkey Thug ammo, and you will not be able to duplicate the performance of Winch LBs at any price. One advantage is that you can load 6s in the 20 ga, while all that is available in most factory ammo is 5s (which is stupid IMO).
If loading HS, it is very difficult to beat EM's factory offerings. One advantage you will have is never having to chase lot numbers, and never having the mfg change the components on you and having to start the patterning process over because the "new" lot number won't pattern like last year's shells. One advantage is that you can do a 6x7 blend if you choose, which EM doesn't offer, but IMO should.
If loading HW, you can easily beat Fed's offerings, particularly in the 12 ga, because you won't be saddled with the flight control wad. You can also load heavier payloads and use 8 shot, which many of us have been urging Fed to do for years.
But TSS is where handloaded turkey ammo shines. You can turn any 12 or 20 ga (even those limited to 2.75") into a gun that will beat any 3.5" 12 ga factory load with a lot less recoil. The 28 and 16 ga become 40+ killers and the .410 can become a bonafide 40 yd gun.
And finally, any time you handload, you remove the obstacle of ammo availability. No worries about not being able to find your favorite ammo either locally or online, and as already mentioned - no component changes from the mfgs. As long as you keep components on hand, you can always load what you need.
Not sure what you mean about kits. You can load turkey ammo on a single stage press, like a MEC 600 Jr. But all you really need is a powder scale and a roll crimping bit to chuck into a hand drill or drill press. Most handloaders use new primed hulls so there is really no need for a loading press. You will need to buy a loading manual to obtain recipes. If you buy TSS, it will come with all the recipes you will need for any gauge.
Hope that helps.