I have been using a CPS loaned 200-400 1.4x the last few days exclusively handheld at various local zoos, both to compare it with other handheld shots from other lenses in my stable of the same animals and to help my case to my CEO (the missus!) that, over the long haul, buying this lens is cheaper than a purchasing gym memberships because I'll actually use the lens! On the handheld front it was far lighter than I thought it'd be, so much so that I actually enjoy shooting with it handheld, that arm-burning sensation at the end of the day has an odd pleasantness to it. My wife wouldn't touch it without a monopod so definitely the hand-holdability is relative.
It is an amazing zoo lens!!! Here in Arizona many of the animal enclosures are large, so much so I routinely take my 400 5.6. As eml58 stated if I zoom in whilst in LR I can tell that many images just aren't as sharp as my 200 2.0 or 300 2.8. However, I ran my favorite 200-400 images, interspersed with similar 200 f2.0 and 300 2.8 images, past family members and they "oohed" and "aahed" appropriately and never once complained about focus (in fairness they likely would have made the same sounds for any images). Many of the shots I couldn't have gotten without a lens change or multiple camera bodies.
This image, shot at 540mm, is a good representation of how sharp the lens can be with an extender:http://500px.com/photo/54954232
This one, shot at 400mm, was a family favorite:http://500px.com/photo/54954252
Here is one from a tiger running towards me, leaping into a pool, shot through a fence, with the teleconverter on:http://500px.com/photo/54956286
The shot isn't as sharp as I'd like (nothing other than cropping done on this shot) but with my primes I couldn't have gotten the sequence of him moving towards me. As he got closer I simply flipped off the 1.4x (I wish the lever was on the right hand side) and kept shooting on my 5D3.
CarlTN: regarding moving away from the camera really fast on ai servo I didn't have any issues shooting the big animals coming or going. Once focus locked initially it kept pace with everything I was shooting with no issues.
Overall I love the ability to zoom in and out, compose a shot on the fly, and pretty much handle most any situation with one lens on one body, especially in the dusty, windy conditions that I often face where changing a lens isn't peril-free or convenient and switching between two bodies isn't ideal. I did miss the 2.8 when shooting mounted sauropod cervical vertebrae indoors but a flash fixed that easy enough.
Conclusion? I'm already looking around the house to see what I can sell Anyone looking for some old Star Wars toys???