She has to have an older version of Flash on hers (11.2) because the later versions on FF / Vista 64 on hers would just crash randomly and have rendering issues.
I'm using the latest Flash plugin on my setup without any problems, however that Dragon City game doesn't seem much different on Firefox on my PC than it does on hers, so I think that scrubs off the "not the latest Flash", "drivers", and "The G620 can handle Flash no problems" points.
I thought about a PC swap when I built hers earlier this year (a year or two after mine), but I didn't for the following reasons:
1 - I feel bad about giving her old hand-me-downs (her previous Athlon XP setup was almost entirely from my upgrades) rather than her getting something new sometimes.
2 - if I rebuilt hers and mine at the same time then there wouldn't be a single working desktop in the house and that could end very badly (I'm self-employed so my PC is for personal and business).
3 - I wanted hers to be as power efficient as possible, partly because hers tends to be on for quite long periods while she's at home, whereas when I go out on business my PC might get to sleep 3-4 times a day.
4 - while I'm not making use of the extra two cores (which I know to work) on my 960T, I'm more likely to make good use of them than she is, I'm fairly sure.
5 - doing a clean install of my computer is a lot more trouble than it is worth, and I don't fancy the idea of "throw in a completely different board and hope it works".
I would say that for people not playing almost-full-screen Flash games, the G620 is ok, today, but my wife abuses her PC a bit IMO (things like Firefox sessions that run for days or weeks on end, tonnes of tabs open all the time - and not just with one Flash clip overall), I think the G620 was a bit over-optimistic, however my thinking at the time was that she had done pretty well with the Athlon XP 2500+, though it increasingly was showing its age with regard to Flash.
I joked once that a Core i7 wouldn't be enough to take her Firefox abuse (memory usage is under control since she has 4GB, it has been easily enough so far, whereas memory usage was a serious problem on the previous setup), but I'm thinking that if the G620 has been pushed this much for "typical" usage already, it's not a good option in the long term (and we like to get say 6-8 years out of our setups before getting a new board*). I'm even considering a Core i5 for her but I'm not sure the finances are good for it.
I wish she would hurry up and try Dragon City on IE9 on her setup to see if it works any better. She doesn't seem to understand that fixing this sort of thing is my hobby and my work, so I like fixing things and learning more
* - and getting access to her PC to do upgrades is like getting blood from a stone, so the plan is "get it right, then hopefully I won't have to battle for it for years to come". Also bear in mind that I have to listen to the whining that her PC isn't working properly "but she doesn't want me to look at it".
I'm also wondering whether Firefox simply isn't up to the task, perhaps because of its poor multi-threading support.