panel type is certainly important. TN Film panels are traditionally more responsive than MVA, PVA and IPS panels. It's a complicated story with response times really. Before overdrive was introduced, TN Film panels easily offered the most repsonsive panels. The other technologies may well have been rated quite low at 16ms, 20ms etc but didn't really offer the same kind of real performance as similarly rated TN panels. TN Film panels became widely used since the days of 16ms panels like the famous Hitachi Hitachi CML174SX for instance. Since this time, they managed to reduce the response time a little, but in reality there was never a massive difference between 16ms, 12ms and 8ms TN Film panels. TN Film still remained the most responsive, with some slight improvements, but to an average user, it would be very hard to notice a massive improvement. Remember at this time, the "response time" was always the best case black > white transition which wasn't particularly representative of the performance as a whole. The response time quoted for TN panels was useful really to show the generation of the panel as there was some slight improvements, and also some improvements in colour reproduction and black depth most notably.
Then came overdrive which changed things a bit. TN Film panels didn't change any further really at the old ISO black > white measurement, they had already been milked for as much as they could at this point. However, grey to grey transitions were greatly reduced and this helped overall responsiveness quite a lot. Modern TN Film panels like 4ms, 3ms and 2ms G2G all offer improved responsiveness over the old non-overdriven panels. However, there isn't really a massive difference between all these overdriven TN Film panels, and again, the quoted response time (now G2G) is still the best case and not really a true representation of the overall performance. To the average user, you could consider it like this:
old generation TN Film without overdrive = 16ms = 12ms = 8ms to an average user, some slight improvements as this quoted time was reduced
new overdrive generation TN Film panels = 4ms = 3ms = 2ms really, perhaps some very slight difference but to an average user all pretty equal in terms of responsiveness
the overdrive application really did help the other panel technologies though. Suddenly, thanks to this technology, MVA, PVA and IPS panels could offer boosted G2G transitions. They still weren't quite as responsive in real use and the "feel" wasn't quite the same as a TN Film panel. However, they became much more suited to gaming than the non overdriven versions. You have to be careful with the quoted response times a bit more on PVA / MVA / IPS panels i think:
Samsung PVA- their 8ms G2G didn't really offer any improvements in real use according to reports compared with the non overdriven version. An example of this is the Samsung 193P+ rated at 8ms G2G, but using the same panel as it's 20ms rated predecassor, the 193P. Overdrive was applied, but didn't really make any difference in real terms. Their 6ms G2G generation (eg Samsung 970P) offered some good improvements though this time. The reports are the same for some of their larger panels. The 24" PVA panel used in the Dell 2405FPW was 12ms G2G, but not reall as responsive as some might hope. The 6ms G2G update for the 2407WFP (already in the ACer 2416W) supposedly offers some good improvements though (BeHardware thought so and compared the two panels). Samsung's PVA panels became responsive at 6ms G2G which is where they are now
MVA panels - these hit 8ms G2G with the famed Viewsonic VP191B. Much more responsive than the old generation MVA panels, and on par with the 6ms G2G panels from Samsung (PVA). These offer comparable performance in real use though to the 8ms TN Film generation from various comparisons.
IPS panels - only recently have new overdriven IPS panels been released, and early reports are excellent. The 6ms rated AS-IPS panel in the NEC LCD20WGX2 for instance is supposedly as responsive as even the 2ms TN Film panels. I'd like to see more reviews and response time graphs but things look promising for IPS and overdrive.
So for these panel types:
8ms PVA = same as old PVA really
6ms PVA generation = 8ms P-MVA = 8ms TN Film (non overdrive)
6ms AS-IPS possibly = 2ms /3ms / 4ms TN Film!
Hope that helps a bit. You have to be wary of quoted times, but that might help show what has happened over the last few years