I haven't had too much time to test the recently added home integration with the Shield. However I do have the 2015 Shield, the 2017 controller, and a Home Mini.

I'd definitely recommend the Home Mini over the controller. You'll get better accuracy especially for the wake command. It'll be much more responsive since you don't need to wait for the Shield to come out of sleep and wake up your TV and/or speakers. Also in general the official Home products get better support for additional software. Also the controller has to remain charged whereas the Home just has to remain plugged in.

The real plus for getting the controller is you'll have a decent controller for gaming on the Shield or you can use it on your PC. And also the assistant is more finely integrate with the Shield, which should matter less and less going forward.

I would see into getting all of them but for different reasons.

First the controller, search on GameStop.com and see if any local stores still have any. They're getting rid of all stock at $25 a pop. I bought a second controller that way.

That being said, the shield controller mic is not as good as Google home device. It's the one thing the shield is actually slow at. It takes forever for it to respond. I haven't tested the new functionality yet. As I really don't use voice to search for content. My kids use it a bit simply because they are very young and it's easier/quicker than typing (4 and 6). Another thing is the actual quality of the mic. My Google home mini in the kitchen often picks up commands over my shield controller. But it's also a race. So if they both hear it, the mini gets to answer cause it can respond quicker.

The only times I use any of these commands are if my hands are full. There's also no mention of if cast enabled devices will get the audio group functionality. So while you might not have a house full of devices now, I must say it's a really nice feature to have. Even during simple tasks of cleaning the house, it's great to have full home audio. With a Google home mini, you can pair it to your AVR, or sound bar through Bluetooth.

TLDR: go with the Google device. Always listening on the shield isn't that great mostly because it takes the shield multiple seconds to respond while any other device will respond instantly and will give you more functionality.

try iwth home mini its best now cause i have checked it many times . its working too good

All of the above. 😬

Like other people have said, the mic on the remote is disappointing compared to other assistant products. I find it not bad per se, but it is a noticable step down and that gets frustrating. Plan to have an alternative within micshot.

I don't really use assistant as we have Alexa absolutely everywhere. However, I do know that google home does not work with the Shield TV the same way the controllers/remote do. The Spot was supposed to bridge the gap, but you already know whats going on with that. Maybe things have changed, but I would look into what features Home lacks compared to a controller.