Before answering your question:
However in my count data, half of the samples are aligned to reference genome using mm10 genome build, and the other half is aligned using mm9(bam files).
Why such situation? Are these different experiments you want to analyse together? If this is the case, you have to take into account batch effects, and depending on the experimental design, it will be impossible to untangle batch effects from your factors of interest.
Regarding your question:
The mm10 genome sequence is better (more bases and less errors) than mm9, and one generally gets more mapped reads when using mm10 as reference genome.
In addition, and more important, the annotation have changed considerably, mostly with new genes added to mm10, but also with gene models changing between versions, pseudo-genes and incorrect annotations being dropped, and some genes / transcripts changing names.
In summary, you have to map the original reads to the same reference genome to proceed with differential expression analysis.