I find the dedicated remote the Google TV ones have quite handy, and it makes it a bit more of a tv-like experience when I'm binge watching stuff.

As for extra features, the remote has a microphone so you can access the Google assistant. They're also full Android devices so you can install apps directly onto them such as games and use the remote as a controller, though I'm not sure how many are supported since I haven't tried that yet. Perhaps more usefully if you have a suitable USB hub and webcam you can use it for video calls, or plug in a harddrive and watch videos from that. Other than that if you're happy with second generation one, I don't think you're really missing out on much.

Wourdn't bother unless you want advertisements or AV1 support (not available on 4k model)

I loved my first gen Chromecast, but I can't recommend the newer ones. I got the 4k model. Aside from the fact that it draws enough power I can't plug it into the TV's USB... it just isn't capable of streaming 4k without frame skips. And no, it's not my fiber internet, the router, or the streaming service. I have a Sony TV with Android TV and it streams 4k just fine. The Chromecast was unwatchable for me, probably downgrading to 1080p would fix it, but then I didn't need to pay extra for the 4k model, and I could have just plugged the standard model into the TV.

There is no should.

You can use it with a remote to browse apps and get suggestions, or cast from a phone. You have to decide if you want that or not, no comparison website will do it for you.

My old Chromecast died and I bought the new one. It actually lets me turn off my old TV remotely without the actual remote. I can turn it off on my phone. That's worth getting a new one for me.

I still have another old Chromecast, but that one is connected to a newer LG TV that I can turn off using the LG app, so it doesn't matter to me.