Im in the same fortunate position with having the 5DMKIII and the 7DMKII.
I bought the 7DMKII with the 150-600mm Tammy and it was a poor combo on the 7DMKII and the 5DMKIII so I bought the 100-400mm MKII and a 1.4 and honestly the 7DMKII its a beast combination. I have just traveled africa for 2 months and the 5DMKIII has sat with a wide and the 7D with the 100-400mm. I shot over 18000 shots in africa alone with it I'm on a 4 month trip.
Infact I love the 7DMKII I find its IQ excellent and it has less colour noise than the 5D and it feels so fast and responsive.
If you are going to use fast bodies get some better glass the 150-600s are great for reach but thats about it in my experience. The AF is so lacking especially on the Sigmas simply because it goes past F5.6 at 380ish mm so its technically outside the AF system at 400mm and above at F6.3, with slow moving subjects they are fine but if there is any movement forget about it. Its even softer on crop its much better on a FF body but I didn't find it worth keeping the IQ is so similar across the board of the 150-600mm out there and the 100-400mm is sharper on a 7D than the 150-600mm on a 5D at 600 with the 7 you also get the extra 40mm with 640mm. The 100-400 is in a different category IMO and its lighter too so a more compact set up.
The 100-400mm is an insane combo just love it I've been shooting Uganda Gorillas up to 6400ISO with it and love it. Heres a few shots. These are all wild animals in national parks and mostly no cropping so also shows how close you can get with the combo. Most of the time I had too much lens with this combo.
The images are compressed with fb unfortunately I haven't had much internet to post them to flickr and felt compelled to reply to this thread.
Currently traveling across Indonesia and went see the Orangutans about 3 weeks ago.
Its been absolutely phenomenal for me, even the ISO i find incredible for a crop camera feels like it can keep up with the 5D until about 4000 and still perform up to 6400 with beautiful results all the apes are at 4000-6400 above.
With the 100-400 +1.4 and both 5D and 7D I have 100mm-860mm with super sharp images the tele even works well with the 7D but I have mostly left it bare on the 7D where it is a 160-640mm and I have only twice wanted more, one was a leopard in a tree in the Serengeti and a black rhino in the distance in Etosha but over 600mm you struggle with the heat rising anyway so the tele was useless.
Its a serious combo and the lightest you will get with 10fps. It amazes me the amount of people who don't like the 7DMKII I use my gear hard and shoot in the most relentless environments and it just never lets me down and the IQ speed and overall quality just keep blowing me away. The 5D feels like an old camera in comparison I just hope canon adds more F8 focus points with a firmware on the 7D and it will be almost perfect. I haven't been let down with DR as you can see in the above images its extremely difficult in rainforests with such hard light and shadow areas because of the canopies.
The 1DX is a natural progression but its too heavy and too big, my travel gear is like 12kg inside and Fstop Loka (really lightweight at like 1.2kgs) with an 11" MBA, charger, 3 HDDs and a bag of cables, 5+7D 24-105, 100-400mm, 1.4x, 16-35mm F2.8, 4 batteries +chargers, black rapid strap and thats my day bag/carry on I also have a 22kg bag with all the rest of my clothes etc. Been on the road for 3 months now and I would not want any more weight with me.
Big whites sound like the solution to all problems but in the real world for most people they just aren't, especially if your traveling longer than 2 weeks and don't have a porter to carry your bag. If your on a specific photography holiday and feel the need to spend 5k+ for that benefit with pros showing you what to do and with the vehicle rigged up with mounts then fine. I decided to backpacking instead of photo tour and everyone I've seen using them has struggled with their size, then there is worry with traveling with them with size and weight. I saw an asian man trying to use the nikon equivalent and it was comical it was bigger than him and watching him struggling carrying it I felt sorry for him.
Try using one in a safari vehicle with 4 other people in it, 500mm are almost the width of a defender/landcrusier with a body attached. I had another guy in a vehicle with me with a 500mm he was so frustrated and my images are more compelling because the lens was small and easy to use and the benefit of a zoom. By the time he got in position the moment was gone.
Most of the time on safari you don't really have the time to sit and wait for the moment to unfurl because it can take hours so you have to try and get what you can when it happens.
Also try treking through Biwindi rainforest trying to find gorillas that like being on 45deg inclines we hiked 6 hours in 40+deg C to find them and with a lens and camera combo like a 1D and 500mm which weighs roughly 6-7kg and using a machete to hack your way through, its really really hard work.
Just my opinion anyway, everyone is different and has different needs.
Hope that helps.
If you want to have a look at a few more just follow the link to my FB page where I have posted the images I've had time to edit/post.
https://www.facebook.com/tomscottphotographycumbria