Lots of replies and interesting ones, in this topic! 
I think the basic framework /ruleset of an OSR game (6 Ability scores, Roll high/random element, explore and build words, adventures of all kinds) can work for almost any type, feel or style of game.
From the most combat heavy, hyper-violent, realistic, dark setting and game to a barely any rolls, little structure, very positive/upbeat, collaborative story telling, non-combat, NPC-interaction heavy, dreamy almost child-like (in a good way) game.
I have run both, and really enjoyed both. But I always run each style only people with that enjoy or ask for such games. Especially a really dark one I would hesitate to run with most people and some themes I would not do or simply skip over very fast in terms of description. After all, most people play RPGs to relax and even grow, not to get bummed out. But I also wouldnât run a dice-less and XP-less, 0 Combat, 0 Dungeon-delving campaign for more than one or two sessions in a hurry. People like some progress, collecting things, a sense of risk or danger, milestones, a sense of goals and accomplishment. These are cool and natural impulses as well, so I like to provide for them in my game and narrative.
As for the board games vs RPGs thing, I personally sort off dislike vast majority of board games yet love RPGs! What I dislike about most board games is that they are very procedural, usually adversarial (there is only one winner at end of board game, rest all lose in game mechanic terms), low on story-telling and or world-buidling (usually have none). The rules are far more rigid than in RPGs, no GM discretion etc. Your options (both in what you do next or how the âstoryâ develops are usually severally limited compared to an RPG. Besides that I donât even think the playing field is level in most board-game sessions.
For instance: usually by the time you are third or half way through the game, you know! who is going to win. The person who drew a few good cards or had 2 good rolls at a critical junction, or even just because they had the better starting position at the outset. Or, the person who owns the game/is most experienced is far likelier to winâŚ
In these very common circumstances, the other 3 players often know it too, that their chances are very small, so they are there more or less there for nothing in terms of being the âwinnerâ. I mean if everyone still enjoys the game, great! But it is not my bag. I want EVERYONE to win. 
That is how I define a game as âcosyâ: everybody âwonâ = had a great time, some valleys and lots of peaks and everyone is thoroughly invested throughout the entire game and afterwards everyone feels amused and elated, not down in any way. Fortunately, the OSR really engenders and often even heavily favours this style of play, sure it can be gritty and your character can die, but that is all the more reason to work together and not try to go only for personal glory or backstab your friends.
I think the OSR allows for everything and it is a very personal preference. The âduality of manâ and âit takes all kindsâ come into play. For example, I LOVE UFC and MMA, I train a tiny bit, yet I donât want that kind of violence in my game necessarily, or rarely. I also love Kittens, dogs and cute stuff all day! And I like having some of that in the game too, it makes people vulnerable and child-like sometimes, which is one of the very best things about playing games as an adult for me.
I think every GM has experienced this when you introduce a cute familiar or NPC, people really bond with this imaginary creature sometimes and want to take care of it or delight in any of itâs antics. I canât think of any other game almost where these type of things happen on the regular, so I never want my game to be devoid of this, but I also donât want it to be 75% + of my game. I, and my current players (3 out of 4 of which love cute and cosy stuff) would get bored.
In terms of the style of play and nature of RPGs, I am always reminded of my favourite qoute about D&D::
"The remarkable thing about D&D is that everyone has to play together. Even the DM, who plays all the monsters and villains, has to cooperate; if he doesnâtâif he kills the entire party of adventurers, or requires players not to cheat on life-or-death dice rollsâthe chances that he will be invited to run another session are small.
Here I am tempted to advance a wild argument. It goes like this: in a society that conditions people to compete, and rewards those who compete successfully, Dungeons & Dragons is countercultural; its project, when you think about it in these terms, is almost utopian. Show people how to have a good time, a mind-blowing, life-changing, all-night-long good time, by cooperating with each other! And perhaps D&D is socially unacceptable because it encourages its players to drop out of the world of competition, in which the popular people win, and to tune in to another world, where things work differently, and everyone wins (or dies) together."
All the considerations in the qoute above also apply to the cosy vs dark RPG game thing. If you are always running a dark, scary and especially a full-on depressing game, people are not going to enjoy that for more than a few sessions, unless they are hyper-edge lords, which I donât want to play with anyway. In such pitch-black stories the players are also likely to cooperate less and tend to become more chaotic or evil, which is a bit strange if you are a party of adventures trying to meet challenges togetherâŚ
You can be very, very dark yet funny, out there, surrealistic or thought-provoking and I think that can work for groups! Examples of such stories would be Horace and Pete and Bojack Horseman. They, on the face of it, are some of the darkest and most depressing shows and stories I have ever seen. However, at the end of watching them I am often smiling, because they are funny, ârealâ and make me think. And they have their very cute or redeeming moments as well. Balance in all things is good.
