According to the supported versions page for 10.2.1b (GIS - Supported Versions - 10.2.1a - 10.2.1c ArcFM Desktop, Designer, Designer Express, Network Adapter, Fiber Manager, Conduit Manager, License Manager, and Object Reader for Desktop), ArcFM Viewer 10.2.1b is only supported to run on a 10.2.1 database. You could try to have ArcFM Viewer 10.2.1b run against a 10.1 database, but you won't get much help from SE if you run into problems.
And it looks like the same answer applies for ArcFM Viewer 10.1 (GIS - Supported Versions - 10.1 - 10.1.1 ArcFM Desktop, Designer, Designer Express, Network Adapter, Fiber Manager, Conduit Manager, and License Manager).
At our utility, we never mix the versions up because it can cause all sorts of weirdness. You might be able to get away with it, since you're only talking the view-only software, but I would never try that with an editor.
David is right, and the combinations are technically unsupported.
With a newer client (I'm assuming you mean ArcFM Viewer for ArcGIS Engine, or VFE) and an older geodatabase, some degree of functionality is likely to be present depending on the ArcFM products in use. Conduit Manager and electric tracing probably will work, Fiber Manager definitely will not.
With an older client and a newer geodatabase, things are much less likely to work, as there will be potentially unexpected fields or formats in the ArcFM system tables that the older software just isn't expecting to see.
Officially we recommend the client and database releases of the ArcFM software be in sync.