Back on the original question, it depends on the Spit9 model. The MkIXF wasn`t a big performer, at low altitudes a 109F would climb faster and be somewhat speedier. At high altitudes, 20 000 ft and above
I`d believe the turning would favour the Mk9, and rolling, particularly at higher speeds the 109F, tough at low-medium speeds roll performance is rahter similiar. Handling favours the 109F, having much better harmonized controls, whereas a Spit pilot had to fly with his aileron controls being excessive, whereas the elevators was so light and touchy, that a mere 3/4 inch of pull could stall the plane...
Despite that, I`d say in the horizontal plane where Spit 9s had advantage, provided it has an experienced pilot who got used to the controls. Rookie vs. Rookie, a 109 pilot could win, his plane being more noobie-friendly than his opponents
It would be the vertical plane where the Mk9 would outclassed, all Spits had lousy dives and zoom climbs, whereas 109s excelled at those. So if the usual 109 tactics of boom and zooming is followed, he has little to worry, and he only takes risk if he engages the enemy in a turnfight, which favours the Spit pilot.
Of course comparing the 109F to a Mk9LF would give the latter advantage in speed and climb, altough relative dives and zooms would change little... but I feel a little stupid to compare the mid/late-1943 Spitfire MkIXLF with the late-1940 Bf 109Fs...