Cruising speed for a He-111P (which made up half the He-111s at the beginning of the war, the other half being early 111Hs) with bombload was 190mph at FTH of 5000m. The H-1 through H-3 were almost identical to the He-111P, but instead of DB engines they had Jumo 211A-3 engines of equivelant horsepower.
You might have a point if you consider post-BOB He-111H models (usually H-6 and later, H-11s+) as far as performance with the Ju-88, but these had later Jumo211D and D-1 and 211F-2 engines in them.
Then again, our Ju-88 is also post-BOB, with too much horsepower, wing area, and defensive guns, to be comparable to what the BOB had in it (and even then, it was a small minority in the LW bomber fleet in the BOB)