The P-38 would have had the same problem in both circumstances. In the BoB you could not have avoided the high flying 109s, no matter how quick you got up. The Mosquito can handle itself in a dog fight, and even then the tactics of the RAF were for the Hurricanes to take the bombers, the Spitfires to take the fighters, this would be the same wiht the Mosquito only the Mossie would be on the bombers.
In the Pacific, the Mosquito would still be able to get up. You make out as if the Mosquito climbs like a WW1 Gotha bomber or something.