You'd be correct in thinking that today's 105 would be superior to your decade-old Ultegra.

However, if you've already got integrated index shifting (the kind with shift levers integrated into your brakes), it's probably not worth upgrading to a brand new drivetrain. New drivetrain components cost an amazing amount, and function-wise aren't too much different from their 1997 predecessors. If your stuff is workin' and shiftin' smooth, leave it as it is.

(I actually really like the older Shimano stuff. Even if technically inferior, older Shimano bits are smooth, solid, and reliable. Hold on to em'.)