at the muzzle maybe, but with better ballistic coefficient, the .30-06 will have the advantage at range...probably past 200 yards the .30-06 will have more energy than the .35 Whelen.
Depends on the bullet, while 35 cals are not highly prized for stagering high BC values there are a few decent ones out there and there are poor BC bullets in 30 cal too, for an accurate comparison let's put them to the test with the same model bullet using heavyweights for both, I have my Nosler manual handy so lets try with the Partition a very popular and highly effective big game bullet. Trajectory is zeroed at 100yd, used 300 yards for the test, energy/trajectory
30-06 200gr Partition .481 BC max load at 2688fps
300yard: trajectory-14.5", energy 2068ft/lbs, speed 2158fps
35 Whelen 250gr Partition .446 BC 2506fps max load
300yd: trajectory -17.7" energy 2132ft/lbs, speed 1960fps
Now throw in the 338-06 with some slick modern bonded poly tips just for fun
338-06 225gr Interbond .515 BC 2700fps
300yd: trajectory -14.2" energy 2421 ft/lbs, speed 2202fps.
And remember the biggest advantage of the 35 cal is the larger frontal area of their bullets making a larger PWC not the energy they carry. Energy is great, but energy dispersion alone is a long way from the fatal wounding, if you don't believe that just slap yourself, you can "dump" a whole bunch of energy with a slap without doing any real physical damage.