How does the Canon C100 with External Recorder compare?

If it's your first cinema camera then yes C100 will be best for you, save money for lenses and such that will be compatible further down the road.

The Mkii does seem to have some useful improvements. 60fps (maybe not useful for narrative), positionable screen and proper view finder could all be useful. The tests I looked at showed improved image and better low-light performance from the new processor.

Its depends on how you like to film. The external recorder will be more detailed but noisier. The encoding taking place on board will wipe out fine detail, but also noise on the low end. If you like to push iso's then don't get an external recorder, you're only shooting 8 bit so noise reduction in post will not be pretty. If you like to expose for 400 ISO and get a beefy negative you'll get more out of the external recorder.

Also, consider the BMVA. It uses inexpensive SD cards so both cost and post-production work is less.

For what it's worth, I work with a c100 on a daily basis, and I haven't seen much of a difference between recording to an Atomos Ninja and recording to SD. I haven't done any extensive tests. I haven't viewed on big screens. Mostly, all I do notice is much, much bigger file sizes, and clunkier and longer editing/processing/rendering. From memory, I think you do see slightly more detail in both highlights and darks when recording uncompressed, but only in a way that's there when you're pixel peeping and looking for it. So, I just record internally instead.

This is what I believe (but I hope someone more knowledgeable will chime in): when you record to 10 bit 422 or whatever, the image is still 8 bit. It's limited by the processor. There might be more flexibility in pushing around the grade in post, but you're not going to see immediate differences. In theory, there will be fewer compression artefacts, but, to be honest, I very rarely notice compression artifacts in ordinary footage anyway.

For relatively still scenes, there isn't much difference between H.264 and ProRes to the human eye. When there's complex motion, H.264 falls apart and ProRes is the obvious winner. Now, I said "human eye" because CODECs are designed to drop information where people don't notice, but a computer will notice. If you're doing aggressive grading or compositing, ProRes has an advantage. Some editors also have the ability to export ProRes without recompression as long as no processing is done to the image, giving further advantage over H.264. Only use HQ mode, BTW, or it can be inferior to H.264 under some conditions

Side note, when recording an 8-bit HDMI signal to 10-bit CODEC, the last two bits are essentially just left as "zeros" and make no difference. It's simply that ProRes has no temporal compression that allows it to look and composite better.