Anything I say regarding police work would be badly dated since I retired in '89.
When I started on the police department, Dallas used single officer cars on the day shift and two officer cars on the evening and late night shift. We rotated shifts every month, so the senior officers worked a month at a time on each of the 3 shifts while the newer officers (for about two and a half years) worked only evenings and late nights; two months on one of those shifts, then a month on the other. I have forgotten the exact date, but in late '65 or early '66, we went to all single officer cars (except when a training officer had a recruit).
Preparations for the change was the best kept secret in the history of the police department.

I still don't know how they did it. None of us patrolman had even heard rumors of the change, but when I went to work at 3 p.m. that day, we had a bunch of new cars, marked, equipped, etc. and they told us we'd all be working alone. There were a lot of very unhappy officers that evening. Keep in mind that in those prehistoric times, we had a 2 channel radio in the car; no cell phones, mobile phones, portable radios, computers, etc.
As Dan said, more marked cars on the street increases police visibility which many believe reduces crime. One theory is that with the officers spread out, they'll see more of what is going on. On the other hand, one officer driving may not see things that a second officer (passenger) might see.
As Dan said, two officers might become complacent. But let's say you and I are partners and we come upon a suspicious and/or quite possibly very dangerous situation. We're going to handle that situation, and right now with no question about it, because I sure don't want you to think I'm afraid, and you don't want me to think you're afraid. On the other hand, when I'm working alone, I might just drive on by and pretend to not see the problem. Why take a chance? No one will know and it pays the same. Yeah, I know; we hope to hire and train officers who won't react that way, but can we count on it?
And what happens when you get an officer who is prone to illegal activity? Again, we hope we don't, but every department does from time to time. He/she may be more likely to engage in such activity when there is no other officer around to see it.
As Dan indicated, I suspect the topic of single officer vs. partners will still be debated long past our lifetime.
