Drop seed is the most accurate, buy takes longer to use. Broadcast is mainly for larger areas, and accuracy is your best guess.. I don't have a big yard at all, so I have the Scott's drop seed spreader. It's annoying, yes, but it doesn't take THAT long for me and I'm not wasting product all over the sidewalks, or putting more down than I should guessing at where to make passes.. also not dropping anything on my neighbors weed patch that is connected to my lawn.. as generous as he is to share all his weeds that I need to fight off every year, I'm not inclined to throw any fertilizer down for him..
I had Scott's chemical service for like 2 or 3 years and it was a complete sham.. I'd put seed down where I needed it, their expert would come buy and kill it.. the last straw was when they just left a bill on my door for doing core aeration and seeding, without ever actually doing that - and exactly what they "forgot" to do the last two season also.. without that, there is really no point to a chemical service..