I've been taking pictures with varying degrees of devotion and studiousness off and on for right around 40 years. Since 2001, I've become more interested in it as a hobby/semi-professional casual portrait shooter/hobbyist/camera nut//freelance sports photographer for two years doing 2 to 3 assignments a week, then later shooting whatever paying gigs I have time for, and in general, really enjoying the "craft" of photography. And yeah, I DO think there are some clearly "better" cameras for portraiture. I've shot with 35mm SLR's (Canon AE-1, Minolta SRT-102, Yashica FX-3, motorized Nikons FM,FE,FE-2, and F3HP; Mamiya RB67 in-studio; motorized fully electric long-roll 35mm camera in-studio for 2 years 5 days week x 8 hrs. day/ 49 weeks a year in-studio; motorized Bronica SQ-AM; Mamiya C220 and C330, Yashica-Mat 124G; and have owned and shot multiple d-slrs for about 2 years each, at minimum: first, Nikon D1, then Fuji S1 Pro, Nikon D1h, Fuji S2 Pro, Canon 20D, Nikon D2x, Canon 5D,Nikon D3x. With a lotta' different lenses. At one time I had two Canon bodies and 10 lenses, including the 24-105 L and 70-200/2.8 L IS USM and 135/2 L, 135 2.8 Soft Focus, 85/1.8 EF, 50/1.4 EF, and a couple Sigmas, an 18-125 for APS-C, Canon 580 EX-II flash. I used the D2x from 2005 until 2012. I also shot the 5D "classic" from 2006 until early 2012. I bought the D3x in spring of 2012. I've also shot a few camera for six months to a year and decided I did not like them much. Nikon F meterless, Nikon F FTN, Nikon F2 of three varieties....ehhhh....
So--are "any" of those cameras better than one another for portraiture? In a word, YES. Are ALL of them equally good for portraiture? NO, no they are most certainly not. Was I able to make nice portraits with all of those cameras? YES, yes I was able to do that. But there actually are certain cameras that work better, easier, and with fewer hassles than others. You can learn to work around almost any limitations in any camera. I've used some very slooow, clunky beasts: Argoflex TLR ca. 1938. Zeiss Contaflex Super ca. 1955. Russian Zenit ca. 1976. Mamiyaflex TLR, 1958. Kodak Pony 135-B ca. 1954. I made one of my FAVORITE pictures with the Mamiyaflex TLR in 1976 of my dad,brother, and grandfather, in natural, summer sunlight, in a boat on the Columbia River. But overall, that camera was tough to use.
NEW, modern, full-frame, professionally oriented d-slr bodies handle FAST, have big batteries and huge memory cards, and accept some of the finest lenses made today. Medium format, like 6x6 square or 6x4.5cm rollfilm is 12-shot on 120 square, and 15 frames on 645, and double that on 220 film. Medium format has slow handling, big lenses, with slow aperture, not many zooms, and shallow depth of field at each picture angle, compared to 135 or "full frame". Medium format digital is not even medium format really....it's more like 127 SuperSlide...meaning the lenses all have crop-factor, AF is slow or absent, and the cameras and lenses are big, and limited in scope/variety.
The thing is, the quality of the light, and the direction the light hits the subject, and where you PUT the subject and the camera, in relation to the light, are keys to photographing in ambient, naturally-sourced light. You do NOT need extraordinary High-ISO performance like the Nikon D4 boasts about; that's for news and sports, where the light is utter rubbish, but you NEED to make pictures. If the light is so bad that you ned much more than ISO 2,000, chances are very high that you'll want supplementary lighting: strobe, LED, speedlight, hot lights, something that you plug in and that runs off of batteries or wall current or an inverter/battery combo. You want a camera that you can SEE WELL through, which is where the high-end full frame bodies shine. You want a camera with a good LCD screen for reviewing. A camera that can handle wide scene dynamic range is super-helpful. You want a camera that handles fast, and is not a total slowpoke.
Best camera for natural light portraiture? It depends a bit, but in terms of preference, here's a rough list that summarizes my feelings, in more or less order from most-ideal for ME, to least-ideal to "ME":
I would say Nikon D3x;Nikon D800 or D800e; Canon 5D-III;Nikon D4 or D4s; Canon 1Ds-Mk IV;Sony A99; Canon 1Ds-Mk III; Nikon D3s; Canon 6D, Nikon D600 or D610; Nikon D3s; Nikon D3;Nikon D700; Canon 5D-II; Canon 5D Classic. I could work with any of those, with my favorite being the D3x for ergonomics and file size and MP count and build, battery, and controls over the D800 or D4. The 5D Classic I used for a long time, but it's the weakest 'body' and weakest "AF" of any of those, and the 5D-II also has rather weak AF under tough conditions.
The fact is that "some gear" just works really,really,really well and is almost transparent in use. Other stuff you need to "ride herd on", or "work around certain issues". As the British say, some cameras are just, "perfectly sorted." Others...have "issues", or "quirks" and whatnot. You gotta buy something you will like, and get some good lenses and accessories. And buy some flash gear too.