There is no chance that XB will launch at a higher price than Sony unless it is much more powerful. More realistically, MS will try to edge out PS in overall "power" (whatever that means), while matching them in price. I think MS will heavily subsidize their system, but only if needed because of Sony doing the same. In fact, if, despite MS' best efforts, PS ends up more powerful, I wouldn't be surprised if MS subsidized the hardware enough to launch at a lower price. MS needs people in the XB ecosystem to drive subscription sales. They've already shown us that they're willing to subsidize for that purpose when they gave up to three years of Gamepass Ultimate upgrade for $1. As others have mentioned, it is tough to see how subsidizing hardware will do much at this point in the gen, so subsidizing the service was the way to go (one could argue that they're still trying with hardware a bit, with the $149 XB1SAD right now). But, that math changes with the launch of next gen systems. I expect they will throw as much money as necessary at pricing in order to beat Sony on one of the two fronts.
Xbox is not MS. Could MS afford to subsidize their HW to $199 and almost automatically win? Sure. Will they, though. Hell, no. They are moving on to streaming. That's why they are giving such deep cuts to push GamePass and probably will for xCloud, too. If they wanted to, they could have subsidized the XBO out of the gate, i.e. a new gen, they chose not to. Not even when Spencer took over did they subsidize the XBO without the Kinect to beat the PS4. And that was in 2014, when it actually could have made a big difference to how this gen played out. Gaming HW is not a big focus for MS. In fact, quite a few of their investors wanted them to drop it. Even Bill Gates said he would be fine with that early this gen.
Also, they don't need to sell HW to push their GamePass/xCloud service. You will always have a few million who will get a Xbox no matter what. And they are putting GamePass and xCloud on PC, a much larger install base. If Scarlett doesn't work out, I wouldn't be surprised to see them put it on Switch, maybe eventually PS5.