Well if it were me, I would mow my yard how ever I wanted and let them b*tch and gripe all they want...it's not their yard and it does not affect them at all!

But then, I have no patience with people like that so there are lots of people I don't get along with, and probably could if I put a little more effort into it.
I do not use the bag on our mower. I push-mow our yard, seeing as how we have a 1/4 acre corner lot, and just make sure the chute is aimed at the middle of the yard. The clippings usually dry up and disappear in a few days, and I hear they are good for the lawn. Either way, they don't bothe rme at all as long I don't let my grass get 4ft high before I mow it.

If I use the bag, even with our tiny yard, I have to empty the bag several times while I'm mowing and it's a huge hassle. Also, I can't say enough for a gas powered weed eater and blower! They have so much more tater than the electric ones.

When I'm done clipping, I go around the perimeter of the yard and blow any fly-aways back onto my own lawn. The more you keep up with the mowing, the less clippings you have.
My opinion could jsut be based on my equiptment, seeing as how I really haven't ever had a snazzy mower or anything, so this is just what is most convenient for me. If you have a bigger mower than I do (prob do

) then you might not have the bag emptying issue I do. If your neighbors' issue is your lawn clippings ending up on their side of the fence, then just blow them back in your yard! And smile and wave when they glare at you from the doorway.

If their issue is with how your yard looks/your method, I wouldn't bother doing anything differently. It probably wouldn't make a difference, and they'd find something wrong with the new way you do it.
I'm sorry you have PITA neighbors! They sure can make life miserable sometimes.