Don't know about dyno runs as never been involved with a cored bike on a dyno but i have setup a fair few Gen2 with a gas analyser and 1 of those was cored so i saw the difference. Basically on variant 2 (open loop) or map 2 as some call it they generally fuel at about 3.5 to 4% at idle when you set them up.
That low speed fueling carries through to about 1/4 throttle or 3-4k revs i would guess. Above that it's purely down to the map programming and only changed by a Pc3 etc.
On the one bike i did that was cored, balance wasn't an issue but the gas reading looked like the bike was on varaint 1 still (somewhere around 1.5 -2%). So much so i sent the guy to get it checked as to what variant it was running (it was on variant 2). He had wanted it checked as the bike was a bit snatchy and he had lots of popping on the overun (often a sign of a lean mixture) and it ran quite warm in traffic compared to similar bikes. Having balanced the Tb's it was a little better but we couldn't do anything to alter the fueling, just balance it.
For those with an axone to look at the ecu, they will see that there are options that you can't enter (password) and those include CO trimming for each cylinder, idle speed etc. I think those are unlocked at least in part on later incarnations of the ecu so it would be possible to adjust further than on the 04/05.
I guess it depends a lot on the core type etc as to how much it effects individual bikes. I would still run variant 2 anyway on a cored can regardless because it disables the Lambda which can only be a good thing if the bike is a bit lean anyway. That is the only difference between variant 1 and 2 is the Lambda, there is only 1 map in the ecu.
The £60 ish you pay for the switch is to change the variant and re balance the Tb's, nothing else can be done without a pc3 etc even with a dyno. I don't know of anyone that can alter the oem map in a Gen2
