They will both sell very well, especially if you actually compare net platforms. If MS manages to have customers on cloud android, PC, Series S and Series X, it will likely even out to PS5. But both may not be as high as expected, depending on what Nintendo does. A strong Switch 2 could cut into both.
Final prediction: MS platforms: 70 Million PS5 platform: 80 Million Nintendo Platforms: 60 Million
Keeping in mind here I fully expect MS to make more net profit with Game pass over the duration of the generation on their 70 million that either Sony or Nintendo does.
Also keep in mind, the fact that MS is not launching Halo might be hurting the image right now, but it might be a blessing in disguise for them if they can put together a good game for next holiday season. This year, all series X are sold out, and likely will be right through to march.
Next year, they can drop the price to $399 and will have the software they need to slug it out. Plus they can move the Series S to $199-$249 - the price the S will most likely sell at for most of it's life. If they can get the S to $199 next year it would outperform all expectations.