The Spitfire XIV gained literally, a ton of weight over the 9/8/16. It weighed a whopping 8488 lbs. with full ammo, fuel (112 Imperial Gallons), oil and hydraulic fluid. It has wing tanks like the VIII, but a larger tail fin, wing strengthening, the mighty Griffon 65, a 5 blade prop, larger radiators etc.
It has a lot of thrust, yes, but not enough to counter its vastly increased wingloading.
The Mk.XVI has lost some 11 sq. ft. in wing area but its extra thrust over our IX and lightness over the IX makes it seem as if it turns tighter. I may have to say that the turning performance listed on Gonzo's page is incorrect for the IX.
But let's take a looksee at the XVI.
231 sq. ft., 6781 lbs (25% fuel, full ammo) = wingload of 29.35 lbs/sq.ft
the Mk.IX is 242 sq.ft., 6843 lbs (same config as XVI) = wingload of 28.28 lbs/sq.ft.
Clearly the Mk.IX has a small advantage due to a lower wing loading but the XVI accelerates better. In reality, you may have just been experiencing a XVI that's turning faster rather than tighter. Ever try fighting an Me163 in a Tempest? Temp turns much tighter, but the 163's X-treme speed gives it a faster turn rate. The XVI isn't quite that fast compared to the IX, but you get the idea. Additionally the XVI has better E-retention. Fighting in the vertical only helps it kill the IX.
Karnak's got a good point. Those flaps cause way too much drag in a horizontal turn fight. The only time I use them is when I need to flip over at the top of a loop. In the XIV, I don't even use them unless I'm landing.