Is it possible to switch between the map that you have downloaded and the original map that is online?? When you're out in the field you might not have signal the whole time. But when you have a signal, it would be great to just switch over to the online map, where you can zoom in closer and so on. But I seem to have problems figuring out how to do it, if it is even possible, when you have downloaded the map.
If I log into my account, I'm only able to see the downloaded map, and not the online map... I could of course just remove the downloaded map, but if I then loose signal, I'm in a world of trouble again.. :)
It seems like once you have the map downloaded to the device, it is not possible to switch between offline and online versions. I would recommend downloading the highest quality basemap to the device and work in offline mode.
To have a more detailed map in the offline mode, you will need to create a TPK in ArcMap and copy that onto the device. Info on creating TPKs is here: ArcGIS Help (10.2, 10.2.1, and 10.2.2). This would require you to have a good reference map with you're own data, you can't create a TPK with any of the ESRI basemaps.
Unfortunately, you can't switch between an online and offline basemap for a single published map in the Collector. The best you could do is have two different published map services that a user would switch between (published maps in ArcGIS Online or Portal, not basemaps). One would be downloaded to the device with lower resolution, while the other a user switches to when there is a connection. This probably wouldn't work too well if the user needs to do edits, since they would only show up on one of the maps until a sync occurs.
Just to update this ... I'm using Collector 17.0.2. I too found that if I downloaded a map to Collector, then made changes to that web map in ArcGIS Online, then I couldn't "Reload" the map on the device. there is a "Reload" option when you are in online mode.
However, there is a "Manage" menu option now in the main app menu (bottom right in Android). There you can remove a downloaded map from the device. Then you just need to refresh the list of maps and the ArcGIS Online version will be there. Make sure you sync any changes first, of course.