I would imagine that it doesn't make a lot of difference, since the area is the same. I think the difference comes in if you're doing a pattern that causes you to backtrack over already-mowed grass.

A practical way to test this might be to take a length of yarn and fold it in rows and see how much area it covers, then spiral it to see if it covers that same amount of area (you will probably need to backtrack some for those corners). In any case, any difference is probably negligible.

My brain hurts now.
 

Say the yard is 100 ft. x 100 ft. and the mower is 30 inches wide. Allowing for six inches of overlap,
the mower must make 50 passes to finish. The average time either down or back is n, so this is 50n.

Making a circuitous route takes 25 laps. There's likely a better way to do this, but it comes down
to:

(4n)+(4(.96n))+(4(.92n))+(4(.88n))+(4(.84n))+(4(.80n))+(4(.76n))+(4(.72n))+(4(.68n))+(4(.64n))+(4(.60n))+
(4(.56n))+(4(.52n))+(4(.48n))+(4(.44n))+(4(.40n))+(4(.36n))+(4(.32n))+(4(.28n))+(4(.24n))+(4(.20n))+
(4(.16n))+(4(.12n))+(4(.8n))+(4(.4n))

I put this at 52n, so going in circles takes longer.

But the fact that it's a rectangle and not a sqare might throw things off. If the yard was 80 x 120
instead of 100 x 100, it would only take 24 passes and therefore a trip would be something like
48n I guess.
 

Lawn mowers don't need gas if you get a manual mower!
 

Yes, of course, the manual mower. I've never tried one--how well does it cut grass anyway?