They are pretty identical in terms of performance. The 8120 isn't really a upgrade.. its more of a newer chip that took over the phenom series. While the 965BE is a great chip and also performs great for games. If that's all your really looking for, then there isn't a need to upgrade.
Another question is do you have a mobo that supports the FX chip. While the 965BE can use some of the older boards. the FX 8120 will require a 8 series or 9 series mobo.
So if you need a mobo to go with the 8120, then your looking to spend more money while not really upgrading CPU performance.
If no mobo upgrade is needed and you have the current chipsets, then it can be worth it just to get newer tech, but not really needed since they perform about equal to each other with maybe the 8120 taking a slight advantage in multi threaded apps due to the additional cores available.