I have been on both sides of this issue before.

I've just moved here from Northern Minnesota and 5 years ago we had only company and our rates were $19.00 per 2 months (we had to provide our own cans) and service was good. 2 years ago, the rates changes to $19.00 per month so I asked the collector on route (who happened to be the owner) why such an increase. He explained that 2 new companies opened up and he was losing business and that he lost nearly 25% of his business and in order to keep his guys working that he needed to pay them more money and get better equipment.
Just before we moved, they announced they were raising the rates again in January to $25 per month and again cited increased wages, costs, and need for more modern equipment.

For the other side, when I lived in California, our city had competition for years and finally decided to go with just one company. I did not notice any real rate reduction in rates as the company cited increased business means increased costs. What did notice is that we had large trucks coming down our streets only once per day. That being said, I've noticed here that rubbish collection seems to occur between 8:30 and 2:00pm when most people are at work and kids in school.

Having been in both situations, I can not tell you that we are in a no-win situation and not going to please everyone.

Oh great! Here we go again with government trying to run our lives because a couple folks don't like trash pick up by more than one company. Hey, guess what you get with no competition? An initial 'good' deal followed by angry citizens over the next several months. But wait, our government will have "locked in" a contract for three years. You know what? These idiots need to get a lesson in working well with others instead of living in their house 24 hours a day being able to hear the competition outside on their street. Why make the rest of us suffer because they can't go talk to their neighbor and come up with an agreed company for their street.
To the PTC council ... Don't waste any more time on this issue. It's dead!!!

When the city decides to open up bids make the garbage companies give the city incentives to be the only game in town. Ask for the moon, and demand as little cost as possible to the city and the residents. It's how it's done in CA. Free bulky pickups per the resident twice a year, fines against the company if they get complaints, missed pickups, debris in the streets. We can do this. Just because they are a business, the city doesn't have to lay down and pick the lesser of the devils if we go franchise.