Third party developer here with contacts at AMD from the old days. Just got our hands on the dev kits and I reached out to my contacts for some backchannel info. Here is what I've got:

PS5 is running on a semi-custom Navi at around 10TF. Performs well but actually squeezing power out of it takes a bunch of work. It's sort of a mess to deal with. Sony really wanted this card and was willing to overlook its flaws.

XBX is running on semi-custom Vega. More power at around 12TF, but obviously using Vega. MS really put a ton of work into it and it looks to be significantly outperforming the Navi out of the gate. From what I hear, the MS team passed on Navi because they felt that they could customize and optimize the Vega and not deal with the headaches that Navi would create. The passed on it.