Like the next Xbox, the PS5 will have eight Zen 2 cores. It will clock them a little lower, at 3.5 GHz rather than 3.8 GHz for the Xbox. But CPUs are so heavy on turbo that the nominal clock speed is fairly dubious. Given that both will have the same CPU cores, if there's a performance difference, it will be due to the amount of power that the CPU is allowed to burn.
On the memory side of things, both the PS5 and the next Xbox have 16 GB of GDDR6. The two consoles handle it differently, however. Sony does the simple, obvious thing: four identical 64-bit channels with 4 GB each, for 448 GB/sec of bandwidth. You get the same bandwidth regardless of how you use it.
As best as I can tell, the Xbox has a 320-bit memory bus, which breaks down unevenly as three 64-bit channels with 4 GB each and two with 2 GB each. That means that if you stay inside of 10 GB, you can get up to 560 GB/sec of memory bandwidth. Go over that, and you only use three of the channels, for 336 GB/sec of bandwidth. That's a lot like the awful shenanigans that Nvidia used to play before the class action lawsuit over the GTX 970 got them to stop. AMD hasn't done that in the past, and I'd bet that Microsoft pushed for it against AMD's advice.
There are a lot of circumstances where, if you really, carefully optimize things specifically for the new Xbox, it will win on memory bandwidth. In spite of that, I'm going to say that the PS5 has the better memory subsystem, due to its simplicity. Programmers hate having to manually put things into different memory pools if there's no good reason for it, especially when the two memory pools will trip over each other because of a lot of shared bandwidth. Apparently Microsoft didn't learn its lesson with the ESRAM debacle on the Xbox One.
As for the GPU itself, both use AMD's upcoming RDNA2 architecture, now branded as Navi 2X. The next Xbox has 52 compute units at 1.825 GHz, for about 12.1 TFLOPS. The PS5 has 36 compute units at 2.23 GHz, for about 10.3 TFLOPS. So on raw performance, the next Xbox wins.
If you read my link above, Sony has some spin as to why their approach is better. Their spin is garbage and they know it. It basically translates to "ours isn't as good, but we don't want you to realize that". More compute units clocked lower wins, because you can get the same performance in less power, in part because the lower clock speed allows lower voltages. By relying on such a high clock speed, there's also a significant risk that TSMC just can't manufacture it to be able to run at the intended clock speed with acceptable yields, and that TFLOPS gap widens further when they have to clock the chip lower. Sony's approach does have the advantage of a smaller die being cheaper to build, which is why they did it that way.
The two vendors are both offering a custom PCI-E over NVMe SSD, but beyond that, they're taking substantially different approaches. Sony is going to fit the PS5 with an SSD that offers high end performance. It would probably be the fastest M.2 drive on the market if it were available today. And they're telling developers that you can assume that the PS5 will have this much performance and it's fine to make a game that doesn't work properly if paired with a slower SSD. Sony will allow you to add your own SSD, but if it's slower than the one you're using, some games might not work at all.
Microsoft, on the other hand, is using a much slower SSD, and possibly only PCI-E 3.0. Meanwhile, Microsoft is saying that you can add your own SSD for more capacity and it will just work. That is, Microsoft isn't allowing game developers to assume high end SSD performance. They've surely got some sort of minimum specs, but they might be set such that every single PCI-E over NVMe SSD ever made is good enough.
I'm going to call that a win for Microsoft. There just isn't much to gain from games assuming that the SSD can transfer data at 5 GB/sec rather than "only" 2 GB/sec. Having real SSD speed rather than the speed of a hard drive, or worse, an optical drive like Blu-Ray, is a huge deal. But even 1 GB/sec sequential and 20k IOPS is really a lot of performance. If that's not enough for a game, the problem is with the developers, not the storage system.
In contrast, the advantage to Microsoft's approach is huge: if you want to add capacity, you can get it more cheaply. And I mean a lot more cheaply, not just a little. If you want to add another 1 TB of capacity with specs analogous to the next Xbox, at current New Egg prices, you can get a Crucial P1 or a Western Digital Blue SN550 for $115. For a PCI-E 4.0 drive of the same capacity, prices start at $200. That right there eats up the PS5's cost advantage from a smaller die and then some.
So on net, Microsoft made better decisions than Sony on the SSD, while Sony made better decisions on the memory bus. For the GPU, Microsoft will give you a better GPU, but it also costs them more, and that's going to get passed on to you. If you want to add more storage than the default ~1 TB that the consoles will come with, however, that's going to make the next Xbox cheaper overall. I'm going to call that a net win for Microsoft on the hardware side of things, but it's not a complete slaughter like the PS4 over the Xbox One or the Xbox 360 over the PS3.