Both.
Box is nice, but only if it is a super nice and sturdy one.
And then, I will probably make a bag to house the deck IN its box anyway - just so that the box doesnot get battered during travel, and to make sure it will not open at the wrong time.
I have made a nice felt bag for my Wild Unknown strong box, and I keep my Bohemian Gothic with its box inside a beautiful bag.
If the box is slightly large and the cards tend to move this way and that inside, I make a very thin pouch for inside, that will keep the cards for sliding around. That is like underwear for the deck
I made that for Prisma Vision, for example.
I would love to be able to do that will all boxed decks, but usually the box is too tight, its just the side of the cards (which makes sense from the manufacturer's point of view).
Tuckboxes are not strong enough - decks that come in tuckboxes, I rehouse in bags immediately. Same thing for big floppy boxes that house deck and book.
If the deck is either made of very fragile cardstock, or is especially precious, I make the bag with a layer of padding, for protection (but it makes the bag more bulky, and a lot of bulky bags eventually take up a lot of room in a house)
I always make bags snug enough so that the cards will not slide around. It gives better protection.
Be it in box or bag, I like to have only the deck, with no parasite like presentation card or LWB (I do not like it when the extra card, the one with the name of the deck on it, gets shuffled by mistake with the rest of the cards).
But decks that come with genuine extra cards (like the Happy Squirel for example, or all Baba decks), I keep the extra card(s) as part of the deck and read with it.
I keep all the tuckboxes flattened in a shoebox, along with all LWB and presentation cards. Just in case I want to give the deck away, it can be complete with its tuckboxe and LWB and all.
I also have a nice wooden box that is roomy enough for a couple of decks in bags, spread cloth, candle, incense, matches, crystals and all. Decks I am currently using live in it, and they are kept in rotation. If I travel, I will take this box, its contains everything I need and gives wonderful protection for everything.
The good quality big sturdy boxes that house some deck and book sets (like Mary El or Gorgon's, or Bonefire), can serve the same purpose as my wooden box. I like them.