No. Project Acoustics isn't a spatial audio solution (at least, not on its own).But MS talked about the audio solution. Read or maybe you don't know how to read. The XSX uses project Acoustics and a DSP to replay the prebaked 3d sound.
They have a separate part of their software stack for spatial audio (see their 2019 GDC talk), which already supports much of what Sony are promising (albeit with a lower object count) on an Xbox One from 2013.
Project Acoustics just provides a highly detailed data set that can be used to drive reverb/etc in a way that's much more detailed and accurate than artist-placed reverb volumes, or anything that could be approximated in realtime (even using raytracing hardware). I highly recommend watching the first Project Triton presentation from GDC 2017, which covers the research that lead to it (Project Triton was the initial research project, Project Acoustics is the final product version) and its initial implementation into Gears of War 4.
Also, Project Acoustics is actually multi-platform, available through MS's Gamestack middleware on Windows, Mac OS, Xbox One, and Android currently, with the presentation from last year promising support for Sony and Nintendo platforms in the future, via plugins for Unity, Unreal, and Wwise (with custom engines possible with additional work).
When MS talk about dedicated hardware to support it, I'd assume that just means some dedicated processing cores (whether that's off-the-shelf DSP cores from someone like Tensilica, customised AMD CUs, or something completely different) that can handle a ton of DSP work for doing reverb, etc, although given that this is MS, I'd expect that to be exposed via an API, rather than the direct programmability that Sony are providing (the same chunk of hardware will likely also be handling HRTFs and other psychoacouatic effects).
I'd expect that Sony will have a definite advantage in flexibility (which they may pay for in future generations when they want to provide backwards compatibility...), but there's not enough data to say who has the more powerful audio processing hardware, since MS haven't talked about that at all (for previous consoles, they've done presentations at HotChips that would include some of that information, but this year who knows how or if they'll present that info).