No friction factors, no differece.
Of course, cross chain could be good for up to a 10% loss.

All other factors being equal, the higher the number of inches, the harder it is to turn the pedals. The difference you present is probably statistically insignificant. We are looking at a closed system. Whether there is a bigger chainring than a cog or the other way around will make no diffence if the number of teeth don't change.

I hope you meant 170 mm cranks! Could you imagine 700s ?

I had your exact same question a while back and while I had no scientific resolution, I did finally settle on agreeing that the larger the chain ring, the tougher the turn. So, the 53 x 23 will seem tougher than the 39 x 17 in your abstractions. I say abstraction, because you really cannot disregard chain friction. Also, I think the “toughness” may well be only off the line, on the start up where you have to mash. Once you get spinning, I can’t see that it matters.

If the gearing is exactly the same, say 60.5 inches, and the chainline is perfect in both instances, a larger chainring and larger sprocket will be easier to pedal because the chain is making a less severe bend around the rear sprocket, and each link is rotating less relative to its neighbor, inducing less friction into the system. This assumes to identical new clean chains, and a new chainring and sprocket.

I'm guessing that the difference in effort is on the order of 1/10 of a percent or less (possibly far less) and would be obviously imperceptible to a rider.

The decreased chain friction could be weighed against the increased weight of the larger components, but since the question was which gearing is harder to turn, we'll ignore that.

So, in short: If the gearing is the same, they're exactly the same to you. To finely tuned laboratory testing equipment, there might be a small, but measurable difference.

Obviously, in your example, the 39-17 is easier to turn.

Cheers,
- Christian

"Assuming gear ratio and chain line are exactly the same, the larger chainring and larger cog will be more efficient. Two reasons:

1) Tension is inversely proportional to the chainwheel radius. As chainwheel size decreases, tension and the resulting frictional losses increase (frictional force is proportional to the normal force between surfaces).
2) The angle of articulation for smaller cogs is larger, meaning that the chain is bending more sharply as it goes around the cog, causing greater frictional losses.

These inefficiencies are partially offset by lower chain speed for a smaller chainring/cog combination.

Decreased efficiency causes decreased chain and sprocket longevity.

In setting the hour record, where drivechain efficiency is very important, no one except Obree has used a 12t cog. Tony Rominger set his records in 1994 on a 59x14 and 60x14."