I think the original question was:
FF body with 400mm + 1.4X = 560mm effective
versus
7D MkII with 400mm, without extender = 640mm (full frame equivalent)
It will depend upon the exact FF and 1.4X being used... but the 7DII without is going to be a stop brighter as well as having roughly "15% more reach"... without added optics. So I'd expect the lens and 7DII combo to be superior in most cases.
If instead you were using a 600/4 prime on one of the relatively recent full frame cameras (say a 6D or 5DIII or later), that would no doubt give superior image quality to the 7DII + zoom at 400mm (no extender). But the FF + 600mm would be a whole heck of a lot bigger and heavier rig (8.5 lb. prime versus 3.5 lb. zoom)... not to mention much more expensive.... $11,000 lens instead of $2100. Would it be "$8900 better"? Not to mention the zoom would be more versatile. Alternative, EF 200-400/4L IS USM with built-in/matched 1.4X... versatile and a half pound lighter than the 600mm... but slightly shorter (560mm with 1.4X engaged) and just as expensive.
If you were to crop a full frame image down to match a Canon APS-C camera, you are actually throwing away a whole lot more than "1/3 of the image". The area of a FF camera is more than twice that of APS-C... about 864 sq. mm versus about 330 sq. mm. So you're actually "throwing away" closer to 2/3 of the FF image, cropping it to match. We did a test of the 18MP 7D versus 21MP 5D Mark II some years ago... same lens, same distance, same subject, etc. The only difference was that the FF image was cropped down to the size of the APS-C image. The 7D's image was far superior. It "put more pixels on target"... full 18MP versus about 8MP remaining of the FF image after cropping. So especially for telephoto work there are some advantages to using crop sensor cameras.... unless you can afford and are willing to carry around big heavy lenses to significantly increase the "reach" of the FF camera.
7DII and 100-400L Mk II is a very good combo. While image qualities are certainly important, there are other factors that can make or break a lens... size and weight, focus speed, "hand-holdability), image stabilization, close focusing ability, manual focus capability, zoom action (if not a prime lens), durability, sealing for dust/weather resistance, balance, internal focusing/zooming, filter size, and more.
The 100-400L II isn't perfect (I'd prefer internal focus/zooming... but that would make it a lot bigger and probably more expensive).
https://c2.staticflickr.com/6/5808/30182389183_cb8b01d0a8.jpg
https://c2.staticflickr.com/6/5528/30182393653_27d5f4961d.jpg
https://c2.staticflickr.com/6/5547/30182404503_9cb5b1432f.jpg
https://c2.staticflickr.com/6/5345/30182409043_130b8d98b3.jpg
https://c2.staticflickr.com/6/5588/30185481134_9144492dcc.jpg
https://c2.staticflickr.com/6/5328/30185483144_1215f02fee.jpg
Those are six out of over 17,000 images I took at a four day event in October, a lot of which were shot with 100-400mm on 7DII. A very fast acting, versatile lens & camera combo is necessary when everything happens in 8 to 10 seconds and there typically aren't any "do overs". I'm not a fan of long, high speed bursts... but sometimes it's the only way to get that one, good image. Occasionally you might even get a series of good images! Unfortunately, Internet resolutions and sizes really don't do the camera and lens justice.
Going from 550D (T2i in the U.S.) to 7D Mark II will be a shock. The autofocus system alone will be a challenge to learn initially. Where you have 9-point AF, one cross type AF sensor at the center, choice of Single Point/Manual or All Points/Auto and a fixed focusing screen.... you'll need to learn to use 65-point AF, all cross type, plus the choice of Single Point, All Points, Large Zone, Zone, 4-Point Expansion, 8-Point Expansion and Spot Focus patterns, as well as an active matrix transmissive LCD focus screen... plus a bunch of user-adjustable focus fine-tuning or customizing options. All this allows users to set up AF for peak performance in a lot of situations... but if set up incorrectly, it can just as easily make for worse AF performance. There's a separate 50 page user instruction manual just for the auto focus system, downloadable from the Canon website. That's in addition to an approx. 500 page user manual for the camera (compared to about 260 pages for the 550D/T2i).
7DII is an "action/sports" camera. It's AF is run the same way as 1D-series.... with a discrete chip. Images are handled separately through dual processors, to make possible the high speed 10 frames per second. Most other Canon cameras use a single processor for everything... including both focus and image processing. (The 50MP 5DS models use dual processors.)
The 7DII also has no easy-to-use "Scenes" or "Creative Auto" assistance on it's mode dial, the way Rebel series like yours do.... It's just got P, Tv, Av, M, B and three user-customizable modes (C1, C2, C3).... and the one "Super Auto/Green Box". 7DII designers basically assume its users will have a fairly advanced level of experience. As "action oriented" cameras, I've got mine set to AI Servo focus mode most of the time and use Back Button Focusing with it. There is no Focus Confirmation in AI Servo mode, so you need to learn to trust the camera, lens and yourself.
I don't know your level of experience, of course. I am not saying "don't get 7DII".... it's a great camera and might be perfect for you. I just want to alert you to expect some learning curve at first. Personally I've been using DSLRs, SLRs and a variety of other cameras for 35+ years, but still went through the initial "shock" myself with the original 7D. I especially struggled at first to learn to use the AF system well. Almost gave up and went back to the simpler to use 50D that I'd been shooting with before. There weren't even any guide books to help, back then. But I stuck with it and eventually figured 7D out.... then used them for five years. Transition to the 7DII was easier, since for the large part it's a bunch of incremental improvements on the original.
BTW, the 80D is also quite capable... 7 frames per second, slightly simpler 45-point AF, all cross type, with All Points, Single Point, Large Zone and Zone patterns. Though it doesn't use a discrete chip to drive the AF like 7D models, it's still fast thanks to a one-generation newer processor than 7DII (as well as a newer, 20% higher resolution image sensor). 80D also has 27 "f8 capable" AF points, where 7DII only has one. (Your camera is "f5.6 limited".... meaning it cannot autofocus an f5.6 lens + 1.4X teleconverter... while both the 7DII and 80D can). 80D has an articulated LCD screen (which also is a Touch Screen). 7DII doesn't (probably for better weather sealing and overall durability). And 80D has more built in "support" for less experienced users.
Hope this helps!
I think the original question was: br br FF body ... (
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