Even with the bike seat. Any other way will no do. Forget above, forget under, to the left or to the right! The handlebar HAS to be in level with the seat, and exactly 20.3712542 inches ahead, no matter what bike you ride. Road bike, dirt bike, mtb, ALL have to abide by that rule that is SET IN STONE!

I believe it is a personal choice, as I enjoy riding sitting up, because of traffic and the with that cars coming out of nowhere. I have a much better view of everythinig around me, sitting up. So my handle bars are higher than my seat.

As a guess, then, you might need a somewhat "racier" riding position for climbing - your current position is maybe demanding too much of your lower back muscles at the higher average torque of hill climbing - but that might compromise your comfort in the flats. Adjustability is probably limited there, though, unless you have an adjustable stem. To the extent you can - maybe flip the stem, adjust spacers, etc. - try a slightly lower bar position to see how it affects your climbing comfort level. Another consideration might be your reduced energy level after a day's work, depending on the nature of what you do. I leave work exhausted most days, and it definitely informs how I choose to ride home.