Bottom line: If you want the best image quality, especially in lower light levels such as at dusk and dawn, you'll get it from a full-frame DSLR vs. an APS-C DSLR (assuming equal generations of technology). If you want maximum reach, you'll get that from a high-megapixel smaller sensor. Pro wildlife photographers make great photos with both full-frame and APS-C DSLRs. You just have to consider your personal priority—low-light image quality or reach (as well as budget, of course)—and choose your camera accordingly.
Ruggedness If you're going to shoot in harsh conditions, you want a camera that can deal with them. The pro models are the most rugged, but many mid-level models are generally rugged enough for most wildlife/bird photography (the Pentax K-5 series and K-30 are even weather-sealed, as are some of their lenses, including the DA* 300mm ƒ/4). Entry-level models are less rugged and not good choices for harsh conditions.
Higher-end cameras also have better shutters. Those of the Canon EOS-1D X and Nikon D4 have been tested to 400,000 cycles. Mid-range DSLRs have shutters tested to 100,000-200,000 cycles or so. Entry-level cameras have less sturdy shutters; many manufacturers don't provide shutter-life estimates for these cameras.
Not all wildlife photos are action shots. For wildlife portraits, AF performance isn't the prime consideration; image quality is. You want lots of megapixels to record fine details in fur and feathers, and you want accurate colors. Again, you can do wildlife portraits with any DSLR, just as you can do wildlife action with any DSLR. But the best cameras for portrait detail would be the newest models with the highest pixel counts, or Sigma's SD1 Merrill, with its unique Foveon sensor that records all three primary colors (red, green and blue) at every pixel site (conventional DSLR sensors just record one of the three primaries at each pixel site, and obtain the missing colors from neighboring pixels via interpolation using complex proprietary algorithms). This means the SD1 doesn't need a blurring low-pass filter over the sensor to eliminate the artifacts caused by conventional sensor interpolation, resulting in sharper images. Note that the Nikon D7100 and Pentax K-5IIs don't have low-pass filters, and the low-pass filter's effect has been cancelled in the Nikon D800E, which could result in finer fur and feather detail. Some pros who specialize in wildlife portraits and don't do action shots use very expensive medium-format digital cameras for the ultimate in detail.