When one says "agility", one also must ask "at what speed". Surely at low speed the 109 could easily outperform low boost P51D in sustained maneuvers, but most combat occured at high speed where the 109 had very heavy control force and thus it's maneuverability at high speed was severely limited where as the P51D dances at high speed.
And the P51D running at high boost at 75"hg with 150 octane fuel had barely worse climb rate compared to late BF 109G/Ks.
But a civil P-51 nowadays with limited power and ordinary fuel would be considerably outclassed by a 109 Buchon in rate of climb, isn't?