Well for me (in Puerto Rico) they have worked pretty well. I am currently part-time and excluding one account that is from a family member all of my accounts came from flyers. I only handed out about 500 flyers total and I received calls up to 6 months later. In my experience it is best to hand out flyers after it has rained and grass is in all out growing mode and always in selected neighborhoods so your operational costs are low. Almost 100% of calls resulted in clients that I still have 2.5 years later. I have been pretty lucky with clients with only 1 being a late payer by about 2 weeks.
Though this isn't the only advertising method I will use (now and in the future), I will continue using it because the price per 1.3k flyers is around $10(black/white, 4 flyers per page and with an imprint service I know) so with just one account I can recover the costs.
Knocking door to door to promote services would get me a wtf-is-wrong-with-you look, would be taken seriously as a nuisance(residential) and possibly a way of telling them to get off their asses and do their lawn.