The image looks perfectly fine when placed in Illustrator, why so blurry in Photoshop? I need to use Photoshop because I'm planning on doing a color replacement. See screenshots for comparison - both feature the same image. Thanks!
Your Photoshop document is too small (in pixel dimensions).
Placed images in Illustrator will retain their pixel sizes since Illustrator documents work independently of pixels. A Photoshop document on the other hand has a set pixel size and any placed image is limited to that size.
If you are only working on the screenshot itself you should open the screenshot file, not place it in a smaller document. If you do need to place the screenshot then increase the pixel dimensions of the Photoshop document.