It's hard to say overall market share without Nintendo. But they're basically in the middle of generations/an oddity because Switch is a hybrid. PS5 and Xbox Series S/X will compete with Switch and Switch 2.
But if you're saying just the market share between the two of them, here's my pre-release prediction.
Xbox Series S/X: 55 million units (34.38%)
PS5: 105 million units (65.62%)
Some people expect a closer race than that, I don't. PlayStation is a more dominant brand than Xbox, especially in Europe and Japan. And it has exclusives, even if they're shrinking in number.
That's a closer ratio than their predecessors have currently
Xbox One: 48.4 million (29.82%)
PS4: 113.9 million (70.18%)
Lifetime Sales Predictions
Switch: 144 million (was 73, then 96, then 113 million, then 125 million)
PS5: 105 million Xbox Series S/X: 60 million
PS4: 120 mil (was 100 then 130 million, then 122 million) Xbox One: 51 mil (was 50 then 55 mil)
3DS: 75.5 mil (was 73, then 77 million)
"Let go your earthly tether, enter the void, empty and become wind." - Guru Laghima