The "big stuff" eh...the $10 and $15 lawns, lol. There will always be a place for these guys. Some people just want the lawn mowed as cheaply as possible. The problem is when they stop showing up because the truck or mower broke down or they just lose their ambition. I don't find myself losing accounts to them but losing opportunities to pick up new lawns. But a lot of people looking for someone new are doing so because the last guy "dropped out" on them and have never had a real professional lawn service and probably never will.
The accounts I find myself picking up are the people who used to mow their lawns themselves but find it just too much to keep up with or those with lawn services that just aren't responsive...don't answer the phone, don't call back, don't do the extras that every week they say they will do next week.