There are many advantages to an airbrush.
An airbrush will deliver much finer atomisation of paint than a typical spray can. This means you can lay down a much thinner coat and not obscure moulded detail. As mentioned above, you can adjust paint and air flow, giving you the ability to paint very fine lines, or apply subtle shading/fading. This can be quite apparent when you look at military models with multi-colour camouflage, and "faded" or aged paint and someof these effects are all but impossible to paint "freehand" with a spray can (yes, you can mask to an extent, but that's another story).
When you walk into a hobby store, you will see racks and racks of literally hundreds of shades of paint. You can use any and all of these, plus anything in between (by mixing) in your airbrush.
Due to variances in manufacturing batches, different characteristics of colours within a manufacturer's range, and a whole lot of other factors, thinning ratios for airbrushing really tend to be imprecise, and are best considered a "rough guide" rather than something set in stone. Personally, I tend to use the "it looks about right" method. I prefer thin paint, but if I mix too thin, then I just adjust my technique to compensate - less "trigger" and spray another coat or two.
Yes, it all comes down to practice.
Many people think that just by picking up an airbrush, they expect to start producing models like they see in magazines and on this site. Some can, but often they are discouraged because it's not the "magic bullet" that they were hoping for. In many cases, the models you see here and in magazines are done by people who have been airbrushing for years.
The first rule of airbrushing: Practice
The second rule of airbrushing: See Rule #1
As with many things in life, if you approach it with a negative attitude, you will get negative results.
Now having said that, ther are certain modelling applications where spray cans may arguably yield a better result. For example, in car modelling, where you have (relatively) large areas of single, solid colours, spray cans may be preferable, especially when you can get an exact manufacturer's match for certain car colours off the shelf "in the can" eg. DupliColor. Many car modellers do use spray cans for their body work.
If you can be specific about the problems you are experiencing, perhaps giving us some example photos, I'm sure we can offer some assistance in correcting these problems.