I owned the 100-400mm f3.5-5.6 L zoom and it is one fantastic lens as long as you don't use a TC.
With the TC, the AF speed drops and for birds in flight, and this does not help. Also, with the 1.4x TC, apart from image quality degradation (just a tad bit), the largest aperture drops to F8.0 with only center point AF on the 1-series bodies. Image quality is superb and the colors are very nice, but you deal with the issue of the small aperture.
If on a budget, and if you are not too keen on using TC's, I would recommend the Tamron SP 200-500mm which sells for around $800-$850.
The Tamron is a very handholdable lens (light on weight) and is very sharp. I was quite impressed with it and sold my 100-400L in favor of the Tamron 200-500mm. You face the same problem with the 1.4x or 2x TC of working with a small aperture and you loose AF with a TC unless you use the Kenko 1.4x Pro DG TC in which case you get AF (but slow AF). The lens is not as fast as the Canon 100-400L, but can hold it's own.
You might want to check out the reviews of this lens at
www.fredmiranda.com or other web sites.
www.Photozone.de also had a favorable review of this lens.
If you want shots of birds in flight and you want fast AF and sharp images (no TC involved), the 400mm f5.6L is probably the best way to go. Handholability is quite good and the image quality was better than a 300mm f4L + 1.4x TC combo.
Another option to consider is a Sigma/Tokina/Tamron 300mm f2.8 lens on the used/new market (around $1500-$2200) which gives full AF with both 1.4x and 2x TC's. You get a 400mm f4 or 600mm f5.6 lens which is quite good for birding.