A diplo, space and culture victories were perfectly possible to grab by a small empire on Civ4 highest difficulty, so i'd say the small empires were quite competitive back then already.
To be fair, I think that depends in part on the question raised in @The QC's earlier post. Namely, how do you define a "wide" empire?
I certainly agree that diplo and culture victories were obtainable by what I'd call narrow (or small) empires – although in my experience the latter ideally meant having at least six cities to help religion spread. Judging by some of the posts on here though, I get the distinct feeling that some folks think that six cities isn't a small empire in Civ 5 / BNW.
The other point I'd raise though is that whilst Civ 4 perhaps also wasn't perfectly balanced either (ie. just like BNW) it at least used mechanics (eg. local happiness) that allowed you to settle a large number of cities in quick time. Just to illustrate, even on immortal, I could find myself in control of a double digit city empire at 1AD, with each city able to grow and build (or whip in) infrastructure or units for the benefit of the empire. In short, Civ 4's mechanics meant that I was making a lot of decisions per turn very early in the game, which easily sustained my interest in the game – and I knew that I could be making even more decisions per turn as I continued in the game.
By contrast, BNW's happiness mechanic quite obviously – albeit indirectly - caps the number of decisions the gamer can make per turn at a level that, for me at least, is so low that I find boredom is setting in by 1AD. Yes I can settle a few cities, but – even if I work hammer heavy tiles - I find that production comes so slowly that there's simply not a lot to do per turn unless I'm waging war and moving troops around. And this has also been something I've noticed in every single youtube LP that I've seen from those I mentioned earlier in this thread. This is of course a direct result of BNW's happiness mechanic which, at 4 unhappiness per new city, means the total population of my entire empire is limited by the spare happy cap I start a game with, unless I can settle a city for more than one luxury (which isn't guaranteed) or discover a natural wonder. To go beyond that means I “have to” and not “can” as @KrikkitTwo notes here:
...you can then begin getting buildings negating one of those unhappiness and allowing the city to grow.
start building happiness buildings unless an alternative solution is available (eg. in trade) to avoid incurring a happiness penalty.
Depending on my map spawn though, that can mean in turn that my tech path is already laid out for me, because I need to pursue techs to unlock happiness buildings or wonders, just to grow my empire to give me a sufficient number of things to do per turn to sustain my interest in the game. Of course, that means I then find myself asking: exactly how much strategic depth is there and how many choices do I really have in BNW if I “have” to do all these things just to provide me with a critical mass of things to do per turn to make the game interesting? In other words, one un-discussed but very relevant issue may well be that there are variations in how much a gamer needs to do per turn to make the game interesting for them. And on that score, BNW (for me at least) fails to make the grade.
Ultimately, I've ended up as a result coming to the same conclusion that @MkLh alluded to: that Firaxis have so far failed to balance small and large empires in Civ 5 and, what's more, I no longer have the ability to play a game (unless I want to jump through some non-trivial sized hoops) which provides lots to do in the early game, courtesy of BNW's happiness mechanic. Now, admittedly, balance in Civ 4 wasn't perfect either – but there's no denying that a gamer had far more to do per turn of Civ 4 on average across their empire, especially in the early game, than in a game of BNW.
And that in turn has had me asking @Gabriel Pyrrhic's question: is it even possible for small and large empires to be balanced? What's more, it's also had me asking another question of Firaxis. Namely, do they have the ability (or desire) in the team to balance small and large empires by enhancing the power of small empires - instead of just nerfing large ones - to at least provide the gamer with the opportunity to play a strategy game with plenty for this particular gamer (and others like the OP) to do per turn if they so choose?
FWIW, I'm sceptical on both counts. Which is why I plan to spend much more time in future playing other games to scratch that grand strategy (or 4X) gaming itch – because, in common with some published reviews, I find that, once the first X, exploration, is finished in BNW, I just don't find myself doing enough of the other X's (such as expansion) per turn to maintain my interest in a game, courtesy of Firaxis' choice of game mechanics in vanilla and their subsequent decision to retain them.