'My thoughts' are normally I only recommend 970~990FX chipsets for the FX CPUs so folks can obtain the optimal performance. Your MOBO can support up to a 140W CPU, so if the beta BIOS includes support for the FX-8120 then it should work.
Problem, the ASRock 770 Extreme3 isn't a stellar MOBO to start out with and so besides it 'running' the FX-8120 @ stock my deeper concerns are OC'ing a very OC'able CPU...
General reasons for updating a BIOS, this falls under (#1) reason:
In short, if you have no problems then my best advice is NOT to flash.
Examples 'when to flash':
1. CPU requires newer BIOS version
2. Non-OS Instability
3. Peripherals e.g. 2TB HDD requires new BIOS.
4. Memory compatibility ; where current RAM is causing errors or stability
IMO, if your current system does what you need it to do then I see little reason to upgrade. Now, if you're a hardcore gamer, do sizable and complex rendering, CAD, or similar intensive work then sure I 'get it' and recommend that you go for it...
Further, if there's no immediate need then wait and see what the Ivy Bridge does and compare prices, but from what I know the prices 'should' remain on par to the current Sandy Bridge. Don't get me wrong, I don't dislike AMD but they really messed-up and oddly for me to say even just for the money to performance the Intel is the better upgrade path. Normally, I would be saying AMD $ to Performance.
Once IB comes out give it at least 2+ months for early adopters to get the bugs worked out. Intel ain't perfect either...