To give a counter perspective: I have two of the old dropcams before Nest took over and released the Nestcam. The old dropcams are basically the same as the new nestcams except they lack the improved IR. They work flawlessly with Nest's new mobile apps (I have iPad and Samsung Galaxy Note 5.) Also the new web app works great as well. The web app is designed to scale on any screen, and looks a bit like it uses mobile UI, but it works fine so I don't think it's an issue. The only thing I've seen change, is that the old dropcam allowed sharing of cameras, via an invite list. Whereas now, with Nest, you have to either do fully public via a url, or totally private. Nest also enabled full 1080 whereas Dropcam had only 720 except when zooming in on a specific area, with "auto-enhance." (This made the camera only record a smaller FOV which sucked.) So they have made improvement, if only one.

There is also Nest Aware which can let you enable alerts/emails that you get when activity/motion/sound happens when you are gone (it will use your phone or other devices to detect when you leave.) You can also disable the cameras when you are home, if you are one of those paranoid people.

I am not paid or affiliated with Nest at all. I just have two cameras that I use mainly to watch my two cats. They have been great for my use. I have gigabit internet. I have not had any issues.