Disc brakes and wider tires are, in my opinion, the only actual improvements over your Jamis, but even these are only really relevant on rougher roads or more extreme terrain like very steep hills. Are you finding the rim brakes on the Jamis to be unsatisfactory? Are you finding the max tire size on the Jamis (What is the max? 25mm? 28mm?) ride too roughly, or you want to tackle some gravel or other loose surface roads?

IF you answered yes to any of these questions then you potentially will benefit from the new bike. Also if you are just really Jonesin' for a new bike and you've got the cash, then a new bike would be awesome.
Otherwise, you can refresh your older bike so it makes a real difference for a whole lot less than $6k. New handlebars, bar tape, saddle, seatpost, tires, pedals, cleats, shoes... and lots more... can easily be fit into a budget well under $6k.