see here :
https://gis.stackexchange.com/questions/62624/questions-regarding-the-processing-of-mosaic-landsat-8
here the link that compare both method :
http://www.faqs.org/faqs/sci/Satellite-Imagery-FAQ/part3/section-14.html
some people prefer to mosaic first and then analysis like me, and some prefer analysis first and then mosaic
you may read to see the differences and make a decision