Andrew R Stewart 

First thig I'll say is the difference in rear shifting between the chain being on the large a\nd small rings is pretty inherent in the way most all rear ders are. Because the cage pivots off center from the guide pulley as the cage plays out or takes up chain length (from having to wrap around the different sized front rings) the guide pulley raises and falls WRT the rear cog under sides. The more links of chain that span the gap (between the guide pulley and the cog under side) the more points of flex (each chain pivot point) there are that have to load up before transferring the side motion (of the pulley) to the next link pivot and ultimately to the cog's teeth.

Second is that shifting to a lower gear is metaphorically like climbing up a ladder. Each step adds energy to the system. To upshift, gravity (or chain tension from both the cage pivot spring and the rider's pedal pressure) drives the chain down that ladder. It's harder to descend a ladder smoothly the to climb up it.

Third, as Steve B alluded to, cables tend to settle in and effectively "loosen" their tension with initial use (as casing ends push deeper into the caps and the inner cable starts to wear a groove into the casing liner around the curves). So generally cables need tightening up after initial use. But as Steve did say your symptom could be that of a too tight cable.

But also it could be a symptom of too much cable friction as it runs from the levers to the der. (Remember the up shift only moves the exact amount of cable that one cog to cog sideways movement of the der requires, yet one can {and often needs to do** move the cable/der further then the exact amount to shift on a down shift). If there's any significant friction in the cable/casings it will show up on up shifting most often. New cables are not exclusive of poor routing, bad casing end treatments, exposure to grit on first rides/car transports and other friction making issues. Is the routing internal? If so sorry to hear that as this is even more sensitive ti friction and harder to deal with.

If you're lucky all you have is a simple cable tension issue and not a bent hanger or two issues going on at the same time. Andu