The shifters you have are the best system because they exit straight off the reel inside the shifter and take a gentle curve. Shifters after this had cables following a more tortuous route and the shifting is stiffer and less precise. All in the name of fashion.
Typical Cyclechat comment.
It's difficult to use a bar mounted light without getting back scatter from the cables on the old 'washing line' style shifters. This has a significant impact on night vision. Also, as someone has already said, it makes use of bar bags tricky.
Whilst I can't speak for early under tape shifters such as 5700/6700, the more modern ones work perfectly with no stiffness, loss of precision or any reduction in cable life.
Like almost everything else in cycling, new technology is better than old with very few downsides. Not much better, but better.
As an aside, a friend of mine used to have a bike with old style shifters that had been converted to under bar tape using what looked like short lengths of flexible v-brake noodle. Seemed to work fine.