Both the camera and the lens are important. In the digital photography world today, manufacturers are bringing out new camera bodies every several years with more bells and whistles and performance improvements. Choose your lens carefully, that's one piece of equipment that will define the quality of your photos. Once you have a lens that you adore and gives you the WOW pictures, you will probably own it for life plus about 3 or 4 or more others.
Two important characteristics of lenses are focal length and aperture. When digital cameras were designed the sensor size was changed in relationship to the 35mm camera for some cameras. Cameras that use a sensor size the same as the 35mm film are called Full Frame Cameras. In that case when a 300mm lens is put on a full frame camera, it's a 300mm lens just like in the film days.
Cameras with smaller sensors such as the Olympus E-1, E-3 and E-5 have a 2.0 Crop Factor. Therefor in the case of an Olympus E-3 placing a 300mm lens give it the equivalent of a 600mm lens. You will find much technical discussion on a full frame system compared to a reduced sensor size system.
That's beyond the scope of this discussion. However, a reduced sensor size such as the Oly E-3 or the Canon 7D (crop factor 1.6) is a definite plus for the bird photographer. You gain a smaller and lighter lens with a longer focal length. Here is an extreme example. Take a full frame Canon Camera and attach the $14000 9.9 pound Canon EF 800mm F5.6 lens and you have an 800mm system.
Take the Canon 7D camera, attach the EF 1.4 extender and the EF 400 F5.6 lens and you have a 896mm system with a cost of about $2000.00 (lens + extender) and a weight of about 3 pounds.
Have you ever tried to swing a 10 pound lens around hand held to catch a bird in flight?