I don't know where people are getting the idea the He112 was overall the better plane than the Bf109 - or by extension the idea that Heinkel's fighters (the He112A, He112B, and the He 100) would have been the best choice for the Luftwaffe's prime fighter in the early war period. Consider:
(1) The Fighter competitions between the Bf-109 and He112A in the 1930's were very thorough. Despite prejudice against Messerschmitt and the general consensus beforehand that the He112A would be selected, Bf-109 was the clear winner in air combat trials. Other than ground handling where it was deemed better, the He112A was heavier, less manoeuverable, and slower. More critically, Messerschmitt's basic light-weight design concept and structure was much more modern than the He112A (very similar to the Spitfire, infact), giving it considerable "stretch" to absorb new engines, armament. Yes, the He112 had a marginally better range (ca. 650 miles vs 500 miles). However, had the He112A been selected in 1936, the Luftwaffe of 1940 would have been the proud possessor of an obsolescent fighter far inferior to the Spit and probably even the Hurricane. Worse, the basic design would have been incapable of significant improvement, which brings us to....
(2)the He112B. To all intents and purposes this was an entirely new plane, which was a deliberate attempt by Heinkel to make a new fighter which emulated the Bf-109's light weight and potential. It was a much better plane than the 112A, at least as good as the Bf-109B-D. However, by then the decision to adopt the 109 had been made and it would have been foolish to switch to a plane which (although as good) was probably not much better. One thing to consider about the 112B. It used a very short-span elliptical wing which, as loads and weaponry increased, would have had to be significantly enlarged to avoir extremely high wing loadings and maintain good handling. Thus, keeping the plane up-to-date would have been much harder than with the Bf-109
(3) The He-100. This plane did out perform the Bf-109, at least as regards speed. However, by the time it first flew in 1938, the Bf-109 was well established in service and the outstanding Fw-190 was under development. If development of the 100 had been pursued, it would have been in competition with the Fw190 for production orders - and few WW2 fighters would want to be in competition with the outstanding 190. Also, I doubt the He100 would have had the stretch of either the 109 or 190. It was designed very closely around a specific DB powerplant and lots of high-tech and unproven surface evaporation cooling. I suspect the advantages of the He100 over the Bf109 would have disappeared by the time it was upgunned and re-engined multiple times - and it would never have been as versatile as the FW190.
This is not to say that it wouldn't be interesting to imagine the British Spit/Hurri pair opposed by a 109/112B twosome in the BoB, or a mix of 109's, 190's and He 100's rising to fight the USAAF's P-38's, P51's and P-47's. or All those Soviet LAGGs, Migs, and Yaks. I don't think this would make much difference however.
Actually, it would be interesting to imagine a WI in which the He112A won a faked completion (or the Bf-109 was excluded on political grounds) and Luftwaffe went to war in 1939 with a fighter based on the He112A - a plane very inferior to all of its British opponents, and barely as good as most French, Dutch, and early Soviet types.
Who knows, there might not even have been a BoB.