Although they are clearly different, the low point on the curve, and the point of tangency will be pretty close together so although the speed to fly may not be identical, it sounds like they will be pretty close.
Actually, no, they're not that close at all. In any event, you'd sought a 'theoretical answer to a theoretical question'; it's probably not helpful to then dismiss the theory by arguing that, for practical purposes, the answers are pretty close!
The aerobat I fly is limited to plus 6 clean and plus 2 with flaps down. The gentleman in the thread is only saying that a slow speed turn with flaps down - (which would of course be well within the limiting G with flaps down - basic airmanship!) only gives a slightly larger radius of turn than a clean high G manoever at a correspondily higher airspeed.
Basic airmanship, eh? Let's examine that more closely.
I don't have an Aerobat POH to hand, but assuming the 1g stall speed to be around 50 KCAS clean and 45 KCAS with flaps fully deployed, then a Va turn nibbling at the stall at the design limit load factor would be flown at circa:
a) 80deg bank angle and 122 KCAS (r=225ft; ROT=53deg/sec) clean; or
b) 60deg bank angle and 64 KCAS (r=208ft; ROT=30deg/sec) with flaps down.
But the reason for using flaps, apparently, was to provide a safety margin. So let's assume we fly at a load factor of 1.75 rather than 2. In that case, the turn would be flown at circa:
c) 55deg bank angle and 60 KCAS (r=219ft; ROT=26deg/sec) with flaps down.
(Edited to observe that I've made no assumption about level flight here, which would necessitate the more complex consideration of power available; obviously, in the flaps raised scenario - option a above - the high induced drag means level flight couldn't be sustained in an Aerobat at that speed)
So which do you think is better airmanship? 80deg bank/122KCAS, or 55deg bank/60KCAS?
Before you reach a conclusion, consider what might happen in circumstances where things don't go according to plan and the nose drops. In case a), the speed at which some primary structure may fail upon application of full control deflection (design ultimate load factor exceeded) is circa 150KCAS. In case c), it's a mere 78 KCAS! How many pilots would have an appreciation that full control deflection in an Aerobat could possibly cause structural failure at speeds as low as 78kts?
Please donīt be appaled by anything on PPRuNe
Advising that a maximum performance manoeuvre be flown with flaps down for safety reasons is both wrong and highly dangerous. You may not like my use of the word 'appalled', but I'm confident it's appropriate.