LVLCHG differs not in climb from VNAV. However it does from V/S. So much as to that it allows you to climb with full power.
While different airplanes may be configured differently, your post is misleading. For the 744:
Any of the 3 modes will "allow" full climb thrust, if the conditions are right for it.
VNAV will almost always go to full climb thrust, unless the next altitude is captured before CLB thrust is attained.
V/S will use full climb thrust whenever the speed and V/S selected require CLB thrust or more. Then IAS will be sacrificed to maintain V/S.
FLCH will use whatever thrust is needed to attain the selected altitude in 2 minutes. If the CLB thrust limit is reached, V/S will be reduced to maintain selected IAS.
FWIW, I almost always stay in VNAV for the climb. Initially, VNAV optimizes acceleration and climb. With the NADP1 profile, the 744 won't reach climb speed until 4000' or higher anyhow, so V/S will be in the 1000 FPM range during acceleration until then.