"With this ammo my 1903 shoot a little tighter groups."
Not really according to that photo - not enough shots. The groups have almost the same spread on both rifles. To show up a statistically meaningful difference it would be necessary to shoot a larger number of shots with both rifles under as near as possible identical conditions - same day, same time, same wind, same light, same shooter, same level of eye-fatigue etc. etc. Put up two targets closely side-by-side. 1 shot with one rifle on one target. Then 1 shot with the other rifle on the other target ... and so one until eye fatigue sets in. THEN compare the two. It looks like both rifles are probably shooting as well as you can aim (certainly as well as I could aim!) and both would probably shoot under 1 MOA with a scope.
Good shooting, good rifles! Don't fiddle with the rifles, but a series such as suggested above with slightly varying powder charges may reveal a load that is an even better fit for all your 30-06s.