Great question for discussion. The answer is YES !... 5p and 3p are expressed in a differential manner depending on the tissue, cell, etc. The reason could be the presence of their cognate targets. So, if the target of one of them is present, the cell will select the expression of this particular form of the miRNA.
Ok, their targets and effects are different in the same cell. However, actually, the main problem is how the cell leads expression of 5p or 3p forms found in the same pre-miRNA differentially?
We know precious little about processing- and more importantly stability- determinants of miRNAs. One aspect of it would undeniably be target association, as suggested by Francisco. The selection he refers to could even simply result from bound miRNAs being protected from RNases. Think BIG Argonaute hiding LITTLE miRNA :-)
My gut feeling is also that a large number of specific and non-specific (hnRNP-like) RNA binding proteins are involved. As their complement changes between cells and conditions, their associated miRNAs could be differentially stable, too.