After the demise of Fredrik, I wanted to manage my collection of CD ( actually nearly 200 ) and Lp ( between 200 and 400, never counted ) : when I'm in a shop I never remember which Dire Straits or Doors I own.
I tried with Music Collector as they have an App. But was not very happy : they use their own database copied from Discogs but all informations are not present : all the composers, singers,... are not present. And they don't manage Lps.
After all this, I decided to manage my collection directly online on Discogs. Seems to be better ( more complete ).
I see today that they wanted to publish an App soon :
You can sign up to be on the waiting list for the iOS or Android beta test from our Discogs App page. Unfortunately there is a limit to the number of people we can invite to the beta test, so you are not guaranteed a spot by signing up. The good news is that the iOS and Android apps should be released soon (Q1 of 2016), so you shouldn't have to wait for very long!
Do you have more info ?