Well aside from the obvious fact that the two generations where born in two very different time periods ( 1960s to mid 1980s for Gen X and 1980s to mid 1990s for Gen Y), the two generations have some pretty different views on life, love, career and just about everything else. Generation X are the the more focused of the two, with their aggressive and energetic approach towards their careers they surged to the top and stayed there. They're great with working with each other and are a generally hard working generation.
Generation Y on the other hand or should I say the millennials are a different thing entirely, they prioritize having fun over alot of things, they are the more selfish generation and the ones that believe that "whatever they do must make a difference". They are also the impatient generation, the ones that are high risk and high reward kind of people.
As far as their mindsets go, what makes them so different stems from the availability and unavailability of technology like ssmartphones and personal computers. Generation X are more hardworking and believe that you should work for what you want, bit Gen Y are more laid back and will simply find a work around to working hard. Social media has really encouraged the trends amongst millennials ranging for their liberal minded beliefs to their open mindedness.
I believe that the core difference in their mindsets stems from their upbringing. Generation X members where raised by parents who'd seen war and probably tried to instill discipline as much as they could, but the millennials are a different thing entirely, they're greedy and overly money hungery. They were most probably raised by Generation X parents who aren't usually as strict as the parents of gen X.