As I understand it, the more inverters there are, the less sensitivity there is to shadows; instead of losing a large group, you only lose one/a few panels. The other advantage of lots of inverters is the quantity of the DC cabling is minimized. All the long runs of wires are AC which greatly reduces the gauge needed and reduces the losses.
Neil, you almost have it correct. The inverter converts whatever DC you have to AC. Charge controllers optimize the output of the panels each charge controller is connected to. In somer cases there's 1 charge controller built into the inverter and it's still may only be referred to as an inverter, though in this configuration it's doing 2 functions. Individual charge controllers can handle any number of panels within their spec, however they will optimize for the panel with the lowest output, hence if 4 panels are on 1 controller and 1 panel is very shaded all 4 panels will have much lower output. The way around that of course is to have a charge controller for each panel, but in the past that's been a very expensive proposition. A single charge controller is fine for a small number of panels that don't have to deal with any shade besides clouds.
I'm very interested in the SolarEdge configuration.http://www.wholesalesolar.com/solaredge.html
This is a very simple configuration. It's strictly a grid-tie because there's no battery backup, which really lowers up front costs, weight, bulk. You need a charge controller for each panel. They are not that high priced and they offer some unique advantages. They allow you to use panels of different sizes and capacities. The panels are all wired in series, to produce as much as 500 volts DC, which means a much smaller gauge wire can be used. It also means the inverter doesn't work as hard.
The safety advantage this system offers is tremendous. All grid tie systems require an on/off switch to be accessible in emergencies per code. It disconnects the inverter from the grid but most systems don't account for the DC that's still present. This is a bad situation for any fire fighters that have to deal with your home. With the Solar Edge setup each controller communicates with the inverter and only pass current when all the handshaking is complete. When you turn off the inverter all DC stops as well. I haven't seen any other setups that address this potentially deadly aspect of solar setups.
With less current to deal with and a simplified configuration these inverters are pretty reasonable priced. The only thing that drove me absolutely insane is when they show the circuit panel in the inverter. Here's a device that should last 30+ years, and like a cyclops there's this one large electrolytic capacitor sitting on the board. Really?