The formula for momentum is [mass]*[velocity]. I once had an instructor call this the "Mickey Mouse" school of physics -- imagine that, if the formula equals a constant, that if one component grows large, what does the other have to do? Shrink. Sounds silly, but I'll use Mickey to this day.
Suppose momentum is 100 kg m/s:
, for . What is ? .
Can you have the same momentum, for say 5 kg? Sure, but since has decreased, must correspondingly increase, to . The momentum remains the same, though.
The only time when the velocity has to be the same, for two objects of the same momentum, is when the masses are the same as well. They do not vary independently.
Make sense? Or did I misunderstand the question?