COW, 159 bytes
oomMMMmoOMMMMMMmoOMMMMMMmoOMMMmoOoomMMMmoOMMMMMMmoOMMMMMMmoOMMMmOoMOOmOomOomOomOomOomOoMOOMOomoOmoOMOOMoOmoOmoOMOOMOomoOmoOMoOMMMOOOmooOOOmooOOOmooMMMmoomoOOOM
Try it online!
How
[0]: n to be decreased [1]: n [2]: n to be increased [3]: n [4]: m to be decreased [5]: m [6]: m to be increased [7]: m
i=>==>==>=>i=>==>==>=< | set up memory cells as above
[ | loop until some cell becomes 0
<<<<<<[->>[+>>[->>+=*]*]*]= | increment and decrement both n and m
]>o | print the reduntant copy of the smaller
moo ] mOo < MOo - OOO ° OOM i
MOO [ moO > MoO + MMM = oom o