Good summary of most of it Backpacker.
ADS-B and Flarm are actually quite similar in principle. Instead of waiting to be asked, the aircraft broadcasts its position (derived from GPS), level and other info in a data packet. Both ground stations and other aircraft can receive that signal. In the case of other aircraft, they can derive the relative position, and display the traffic to the receiving aircraft. I think Flarm might even do some track processing.
The difference is that Flarm is an uncertified system that works in the Industrial, Scientific and Medical band (garage door openers usually get mentioned at this point). ADS-B can be implemented over different datalink types. The one that will be used in Europe is the 1090 MHz Extended Squitter system, the same one that transmits that data in response to a Mode S interrogation. In fact the formats differ very little. In principle many Mode S transponders will simply be able to do ADS-B over 1090ES. However some, like the GTX328, don't connect to the avionics bus, so won't be able to.
In the US, a new datalink technology was developed, called UAT. It has the advantage that in principle it has higher bandwidth than 1090ES, so the intention is to use it for other data (like weather). However, IIRC there isn't available spectrum at same frequency (978 MHz) in Europe. There's also no technical reason why it should be a cheaper box than a 1090ES box.
Mandates for Mode S and ADS-B are undoubtedly on the way (Mode S has been required for IFR in some controlled airspace for a long time now), though who will have to carry what and when is not yet clear.