The AMI kit looks very nice. Biggest difference is Dany's kit has an actual mechanical switch. Its head is identical to an actual U47 allowing for easy capsule swaps but that doesn't give much advantage if you don't have a U47 to swap with.
I built mine to have variable patterns then the back capsule is switched on. Cardioid only when the switch is disconnected. I modified mine to have U47 voltages though, instead of U48. This can also be acheived with a relay if you want to go with an AMI power supply.
Regarding the AMI U47 kit, this information is incorrect. If you visit
www.tab-funkenwerk.com you will discover U47 or U48 headbasket with mechanical switch options, available for a few years now. All AMI's U47 mechanical parts are 100% compatible with historic Tele/Neumann U47/48.
Dany's kit is taller, so the body and 3 rails are not historically compatible. Fairly sure all other parts in Dany's kit are compatible.
Unfortunately AMI's mic kits are backordered, so not currently an option.
Also for clarity, you do not specifically need a AMI PSU to incorporate a relay in the circuit.
As many of you know Dany is a nice guy and if he has the parts in stock it's a good option. Flea is also a good option, and fairly sure Flea's mechanical parts are also historically compatible.
These are 3 best options for a proper DIY U47/48.