I'm also one of the authors of RaMBLE, another BLE app (https://play.google.com/store/apps/details?id=com.contextis....). It can run in the background, and can export logged BLE advertising packets and geolocation data to a SQLite DB.
I've implemented a UI hint to make this more obvious, which will be in the next version of RaMBLE.
Another thing I just realised is the number of new devices in the notification label. Let's say I put ramble in the background. After 10 minutes it tells me that there are n_1 new devices. I click on the notification in order to check them out. If I then put ramble in the background and it finds n_2 new devices then the notification says that there are now n_1 + n_2 new devices. I would expect that it says n_2 devices.
If you export the database you can pull some more interesting numbers out, e.g. http://www.contextis.com/resources/blog/bluetooth-le-increas...
I have no idea if it's particularly good in comparison to others, but I downloaded it to debug a Bluetooth LE device I was building and it was a pretty straightforward UI.