I have Scorbit on my Dialed In which I bought a couple of months ago and just got a Godzilla Pro with Stern Insider last week so not alot of time on it.
With limited time on Godzilla so far, I still prefer Stern Insider. I find it's better integrated. I get a call out, in game, when achievements are collected with a graphic during bonus (I believe or is it end of game?). With Scorbit, the name of the achievement doesn't always make sense and I don't know I have the achievement unless I look at my phone.
I like the idea of achievements which both accomplish. I like seeing my high score for a given game by accessing the app/website on my phone
I prefer Scorbit app approach over Stern website approach for viewing history, high scores, etc. I also prefer scanning via the phone with Scorbit as opposed to the scanner on the pinball like Stern, but this approach may result in the better integration I mentioned.