It is personal choice up to a point. But also personal choice for the hogs – some don’t like going into boxes, etc. If you want to watch them feeding, then it is probably better outside, unless you have a camera inside the box. (I am taking it that you don’t mean inside your house – that would not be a good idea – it isn’t good for hogs to become too habituated to humans, for various reasons. But if you had some sort of outside shelter that would be o.k.)
Cats are very clever at getting into boxes if they really want to. Even through surprisingly small holes. I have heard people say that they have certain sized entrances that cats can’t get into, only to find one here manages to!
The best all round thing I have found is to put sheets of clear perspex type material onto either bricks, or I use flower pots full of soil. (3 litre one end and 2 litre the other to try to allow for a bit of run off of water – but you might need to change this depending on how big the hogs are – I only have a non-hibernator visiting at the moment – not as big as some) High enough for hogs, but low enough to deter cats. It needs to be weighed down on top, of course, otherwise the cats will just push it up. You will get the occasional cat who tries to get underneath, but it really doesn’t look very comfortable and most seem to think it’s not worth the effort and usually don’t try again. If you could put the set up against a wall and put the food as far back as possible that would probably work best. I had a hog here who didn’t like boxes, but he didn’t seem to mind the perspex arrangement as it was fairly open.
Of course you can’t see through that as well as completely in the open, but at least it deters the cats, so maybe could be put out once you are no longer actually watching in person – if you want to leave the food out. In the past I have only left the food out for a few hours each night so I could keep an eye on the hogs and scare away any cats, etc. Feeding is supposed to be supplementary and I found with that arrangement the hogs got to know when the food was around and visited then. They then had the rest of the night to forage for natural food.
Good luck with the hogs.