Shorter is better except....

If the fan is external, than a longer route may allow a silencer to be placed in between fan and hood reducing some noise.

If the area of the circular duct is significantly larger than the area of the rectangular duct, then pressure loss may be lower with the longer path.

A roof mount may keep the exhaust away from where it isn't wanted.

Many other factors relating to installation ease come into play, so there is no really simple answer.

kas

Everything kas said is an excellent answer to the question you posted.

But ...

I wonder if you meant to ask a different question?. Maybe something more along these lines:

"We are buying a regular range hood to mount on an outside wall in our kitchen. It has rectangular 3" x 10" ports. Installation will be much simpler and much less expensive for us if we vent straight out the back with a rectangular duct through the outside wall. I've heard that round ducting is preferable to rectangular. With this kind of hood, will there be any performance gain if we use the vertical port and coupler and run 6" diameter round duct vertically through the roof?"

The answer: no. The rear vent will give you the best venting performance.

Will there times when you might want to do things differently? Sure, but you won't be doing them for better venting. You will be serving some other objective, such as noise reduction, as Kas mentioned. In those cases, you will be trading some venting performance for something else.

So, going straight out the back seems like the best solution for you.

Current kitchen (soon to be redone) has vertical, rectangular venting as it offered a more shallow vent box (3" depth x 24" length) behind cooktop upper cabinets which then turns 45 or 90 degrees. Round duct is preferable for less effluent in nooks and crannies, amongst other if you're starting from scratch but we aren't.