The AMD 6 cores are beasts in H264 / AVC encoding. They compete well and beat many of the Intel processors in H264 video encoding, as well as being priced well. H264 encoding is one of the few processes that will truly utilize and max out all of a computers cores.
From the Athlon X4 620 you will probably see a very significant jump; I'm sure you can find handbrake benchmarks for both but Passmark is a multi-threaded benchmark and has the 620 at 2986 and the 1100T at 6305... over double the performance. And the 1100T competes well with high end Intel offerings in handbrake, and is supported in your current motherboard.
Your question is pretty much answered but I figured I would chime in since I went from a 620 to a 1055t myself. The difference is what you would expect with handbrake with regards to scaling. (ie the two extra cores and additional clockspeed provide the expected performance increase)
The 1055t does not have an unlocked multiplier so it is harder to overclock. The 1090 and 1100 are the same with unlocked multipliers, besides clockspeed difference.
Based on the last prices I checked, the 1055t is the best deal, the 1090t is worth its price but the 1100t is overpriced compared to the 1090t for such a minor .1GHz bump in clockspeed (~3% theoretical performance increase) at stock.