I suspect, but do not know for sure, that the cloud to cloud option is there primarily for smartthings customers who do not have a smartthings/Aeotec hub. And remember at this point that’s over 90% of smartthings customers: they have a Samsung smart appliance, or television, but not the hub. You can still have a pretty nice setup in that situation, including using hue sensors and smart bulbs, Meross or tplink kasa WiFi smart plugs and switches, ring, Arlo, ecobee, etc.
So I think the biggest difference is just that you don’t need a smartthings hub for the cloud to cloud option.
Logically, you would think that the local LAN option would be more reliable, and perhaps a little more responsive, But since we are in the middle of a huge architecture transition and the official LAN edge driver for Hue is not ready yet, it’s hard to say for sure.
On the other hand, there is a community-created edge Driver using the Hue hub locally with a smartthings/Aeotec hub which has a lot of features that the official integration does not, including the ability to use rooms, groups, and scenes created in the hue app. So I think that’s the most feature-Rich integration right now.
But again, since the official edge driver isn’t completed yet, it’s hard to know for sure what will be available in the future.