|Red = HR, Blue = speed|
Yellow = power, Green = cadence
This graph from a recent ride caught my attention because it shows this tend very clearly. HR increases slightly while power, speed, and cadence all decrease noticeably during each of the three periods of standing. This graph is from a roller ride so the conditions are different with regard to speed and power change; speed and power wouldn't decline like this on the road, but I like to remain on the rollers so this naturally what happens when I'm stretching out. While the increase in HR is small, it's still noticeable and all the more telling since power declines.
The reason for this increase in HR is that you are activating additional muscles to do work, and a rise in HR can be expected when recruiting additional muscles to do work. But similarly, it means that you're using additional energy to supply these newly working muscles that aren't necessarily putting more power in the pedals.
So keep in mind: when max power is the goal, standing may be your friend. But when it's time to conserve energy, seated is the way to go.