I honestly think my productivity is a lot better in Windows 8 then in 7. The updates to search are fantastic. You simply hit the start key and type what you are looking for. You get smart filters on the right that allow you to filter by type (files, apps, settings) and even by app. I have also found that managing multiple desktops (something I often do for work) is made a lot easier by the hover corner. Plus, everything just looks so much better. Once you get the smart tiles up and running to your liking, there is nothing like it. Sometimes, I just toggle the Start screen to see the weather, news, etc. Very cool.
On every version of Windows I've ever used, the search indexing service steals precious background disk and CPU cycles, and almost always causes issues with the two main things I use my computer for: gaming and music production. I can't even count the number of times that the search indexing service spun up in the middle of a gaming session and made my system start to lag. Of course they say it runs as a low priority process, but heavy disk access is going to give you performance problems in CPU/GPU intensive games. Making music is no different - heavy disk access makes it that much more likely that my system will have audio dropouts or in some other way ruin my recording session.
I've disabled search indexing in every version of Windows. In Windows 7, it even makes the start menu almost non-functional because you have to make 3 clicks just to get to the Run dialog.
Anything you need a Run dialog for, you can just press the Windows key and start typing. Everything in your path shows up, with "recently used" suggestions on the right side, and quick feedback if you mistype something.
I'm not sure either lifted it from the other. The concept was around with third-party apps for XP and built into Vista, but it's a feature that's gotten so ubiquitous (spotlight, unity dash, windows search) that it's difficult to say who came up with it first, if anyone did.