I have a Nikon D750 and D7000, and a sigma 150-600 lens that I use for wild life photography.

For a long time my understanding was that for the same lens, a cropped sensor camera has a longer reach compared to full frame. There is an "equivalent focal length", in this case 225-900mm. Taking wild life pictures with the DX camera is preferred because of this.

But then I read that lens focal lengths don't change. The term equivalent focal length is misleading. It really is angle of view. Because full frame camera has a bigger sensor (in this case 1.5X). It captures more picture compared to cropped frame, and gives the illusion of less reach.

Also the D750 is 24 megapixels, compared to 16 on the D7000. Even considering the sensor size differences, the "Megapixel Density" are identical. This means that if I start cropping the pictures from both cameras, I should get the exact same resolution - even though I am cropping more on the D750.

Therefore I should not be using the D7000 at all - wild life or otherwise. For lens reach/picture resolution there is no difference, and D750 offers so much more.

Is this a valid? I like to get opinions from fellow UHHs.

The D7000 does still give you more pixels on target than the cropped D750 image when using the same lens. In excellent lighting conditions the D7000 image will be slightly better. However, in less than optimal light, the vastly better sensor and processor of the D750 will perform better.
I use the D800E as my workhorse, but still carry a D7200 for those times when I need more pixels on target with a long lens (Soon to be replaced by the D500).
The field of view (angle of view) is indeed what actually changes due to the smaller area of the crop sensor. When the "crop factor" of that sensor is applied, the 35mm "EQUIVALENT" field of view is attained, i.e. 600mm x 1.5X = 900mm. All this is telling you is that a FF camera would have to be using a 900mm lens to get the same field of view as you are getting on your crop sensor body. So no, it is not misleading so long as you understand the math and principal involved.

Do what I did. Go outdoors and hang a magazine cover with pictures and small print about 50 ft away. Set each cameras on the same tripod and use the same lens at iso-100, full zoom with the same lighting conditions and f stop in aperture mode on both cameras and take a couple of shots with each camera. The camera will adjust the exposure time that suits it's sensor. See which shots are best. That should answer your question for once and all.

I tried it with 3 cameras with FF, DX (1.5 crop factor) and CX (2.7 crop factor) sensors and my 55-300 lens at 300mm.

My experience is that the longer equivalent focal length trumps the shorter. Cropping the FF and DX images down to the same angle of view as the CX image, I got more fine detail with the DX than with the FF, and more fine detail with the CX sensor than the with DX. The equivalent focal lengths were 300mm for the FF, 450mm for the DX, and 810mm for the CX.

When I compared the file sizes and number of pixels in each of the images cropped to the same field of view, I found the CX image was about twice the file size and had more than twice as many pixels as the DX image, and the DX image was more than twice the file size and had more than twice as many pixels as the FF image. The FF is a 14MP sensor, the DX is a 14MP sensor and the CX is a 10MP sensor.

Have you tried cropping a D750 pic to the same field of view as a D7000 pic taken at the same distance with your lens at full zoom? Were both pics the same size with the same number of pixels? Does the D750 cropped pic have the same fine detail resolution as the D7000 pic, when both are viewed at full size? If so, then you don't need the D7000, but I would rely on my own eyes rather than a theory. To paraphrase Einstein ... In theory, theory and practice are the same. In practice, they are not.
Bob