

I would find it hard to make a general judgement here.
The human-analogies some people make are rather unconvincing. I’d think physiologically cats are less diverse than humans are. In both species size translates to weight, force, reach.
There are outliers, but most house cats are still “fit” enough not to suffer massive disadvantages.
So it would be more a matter of size and stature than lifestyle. A Main Coon with their voluminous fur might enjoy a form of natural armor. But the same fur would exist if it was a street cat (bar any diseases).
And they also possess natural weapons that are not related to their grooming and lifestyle (much). If some jerk has their house cats declawed, maybe. But usually claw is claw and tooth is tooth.
What will probably be the most decisive factor, just as it is in humans, is aggression and killer instinct. That is where a street cat might be better conditioned. On the other hand, animals lean heavier on instinct and even the gentlest house cat can become vicious when exposed to the right stimulus.
tl;dr I am not sure
Besides what was already said, I’d like to add that with only a few exceptions (most notably Japan and to a lesser degree the Netherlands, I believe) most constitutional monarchs even pay taxes on their private income.
They usually receive some kind of stipend/grant as a sovereign which is not taxed. But what they gain from “extracurricular” activities is fair game.
And I think it is worth keeping in mind that a lot of the trappings and estate of a monarch would have to be upkept as part of the cultural heritage and national prestige anyway.
So between paying for a museum/cultural heritage site and letting someone who is essentially a paid actor who got the job through their parents live in there, why not.
And you can never underestimate the soft power a well-liked sovereign can have as a symbol and tool of population control. If the personification of your state talks to the people, many listen.
In international relationships, a monarch can be a soft diplomat and fulfill the role of someone who is at a special remove even from other statesmen and can do and say certain things in certain ways.