BlueFireZ :
Both will do the job fine taking photos of wildlife and portraits. The Canon 750D is a better camera even though the Nikon has slightly better specs on paper.
The 750D greatly outperforms in terms of color accuracy and also video - if you ever think of doing that in the future. Not to mention there are more lens options for Canon than Nikon, and once you become more confident with a Canon DSLR you can even install Magic Lantern (a 3rd party firmware) which gives you more features than the stock firmware. One last thing to add in is that Canon cameras are generally more easier to use compared to Nikon cameras which can be a little frustrating at first.
The above is almost entirely BS. It is so far off the mark that it is just funny. The canon's do not have more accurate color, it is the opposite they have less accurate color and less dynamic range (meaning they capture less color detail).
Don't take the previous Canon fanboy's word for it, or mine either.
Here is the scientifically measured capabilities of the sensors in both cameras.
http
/www.dxomark.com/Cameras/Compare/Side-by-side/Canon-EOS-750D-versus-Nikon-D5500___1010_998
EVS = Exposure values. The Canon is 2 exposure values behind the Nikon. Which is to say 1/4 of the available data in comparison to the Nikon.
Read up on exposure values here:
https
/en.wikipedia.org/wiki/Exposure_value
The Canon has 22.7 bits of color data while the Nikon has 24.1, again a non-trivial amount.
The Canon is the worst in class (for APS-C sized sensors) for ISO noise, while the Nikon is at or near the top.
I have owned DSLRS from both brands and switched to Nikon in around 2008 in large part due to the ISO noise issue, which remained the same pisspoor values for Canon for close to a decade. I can say without a doubt that the Canon is not easier to use than a Nikon. They use nearly identical feature sets and nearly identical layouts.
Canon's do auto-focus faster in video, but since both those cameras SUCK in video autofocus that is more like saying the Canon sucks slightly less in video. Video quality from both is good, but due to the AF speed video fans prefer mirrorless cameras for video (like some of those from Panasonic or Sony).
I don't own stock in any of those cameras. I still own one of my Canon film cameras along with some Minoltas. But I don't use them. I do use several different Nikons for still images and a Sony and Panasonic for videos.
When it comes to cameras, you should read up on several models and hold a few of them. They don't feel quite the same in your hands. I think the Canon has better ergonomics because the larger grip suits my hands better. There are Nikon models with larger grips, but I am comparing the models you listed only.
I am not much of a birder, that is sort of a specialized skillset. I do mostly sports and landscapes. I go however do the occasional bit of birding and the same with portraits (I have studio lights, but prefer natural light)
A bird
https
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A portrait
https
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For birding, you are going to need a LONG lens. (Telephoto) In general I like the Tamron 150-600mm as a low cost long lens (costs $1100). The Nikon 200-500 or 80-400 and Canon 100-400 are also nice but more costly.
For portraits you are going to need a good lens with a large aperature. Most love a 50mm with a f/1.8 or f/1.4 max aperture. If you can get the Sigma 50mm f/1.4 art. Avoid the Canon 50mm f/1.8 as is it cheap and nasty (but cheap).
Not mentioned but if you were thinking birds in flight you would be better served by a camera with a more sophisticated AF system as tracking a bird is tough for any camera and the two you selected aren't ideal for BIF.