Title says it all. This is the question I think.

This year we had COD Ghosts (720/1080) AC4 (900/1080) and BF4 (720/900) show notable resolution differences, even if no real graphical differences. Three of the biggest recurring franchises in gaming.

Many other games like NBA2K14, Fifa 14, and NFS Rivals were 1080P on both and nearly identical. However note these were somewhat less demanding games arguably.

So will the gap close or grow in 2014?

I definitely say close. I even venture that eventually all major multiplatforms will be the same resolution on both.

I think developers will learn the Xbox better, with it's more complicated ESRAM setup it will take more time to learn. In addition, I feel MS will streamline the XBO drivers and reduce OS reservations to gain more performance (because they have to, lest be mocked by PS4, I imagine this is an area of concern within MS and thus they will work hard on it). Thuway says a January XBO update already gains 10% performance. Plus, the usual way of multiplatforms is parity, it's always easier on the developer (note even 2013 XBO versions with less resolution are otherwise mostly identical graphically to the PS4 versions, proving the point of so called "lazy devs").

i dont understand why people think that developers will know the Xbox One better and improve performance on it but wont do the same for the PS4? anyways, it could go either way, depends on what the dev choses to do. The PS4 version of every game should perform better or look better, or probably both. if the devs want to push their games to the fullest extent, then the PS4 versions will look better. if they want parity then that is what will happen.

You're funny. the xbox and ps4 will probably both make their OS more efficient. But let me break down the power for you. It's not speculated that the ps4's CPU is clocked at 2ghz vs the xbox one's 1.75. They're essentially the same cpu, so that's a 14% plus over the xbox one. The gpu's are 1.84tflops vs 1.23tflops. Which creates is a 49.6% difference. The PS4's memory bandwidth is about 3 times higher than the xbox one's. On top of all of this, the ps4 has a seondary chip that takes care of side tasks during gaming. On top of this, 10% of X1's power is reserved for the kinnect. So, with all of this, the only thing the x1 has over the ps4 is 32MB esram. Let me put 32mb in perspective for you. The xbox one's total pool of ram has 8224MB of ram. That means the esram makes up a woping .39% of the system's total ram. The esram isn't even that much faster the the ps4's gddr5 either. I think it's 170GBps  vs 190GBps. So about an 11% differnce in speed. Also, if you want to keep telling yourself the resolution makes no noticable difference, you can keep telling yourself that. It's pretty easy to see if you have eyes. Why do you think most PC gamers will lower other settings to get a higher resolution? It makes the most noticable difference. Also, all of those games you mentioned with the ps4 having a higher resotuioin, the resolution isn't the only difference. Look at screenshots of the ps4 and xbox one versions of BF4. The xbox one version has lower res, less AA, lower texture details, washed out shadows. This is also applicable for every game you mentioned. And those are details I could spot from compressed videos. That means the difference in graphics is even easier to tell in person because it will make the better graphics look worse because it can't show as much detail from it. So if you want to keep fooling yourself into believing that the eSRAM is going to make the xbox one twice as powerful, you can keep fooling yourself into believing that. 

no.
Casuals don't giva two fucks about resolution. If they did Killzone should outsell CoD 10:1

killzone and CoD are the same res on the PS4

How about now?

imo, depends on how well xbone sells relative to ps4.

if ps4 dominates the market it will be the lead platform for development and xbone will get shitty ports because MS will be in a weak position. if xbone can keep pace with ps4 developers will put more effort in because MS will demand parity and will have a stronger position to negotiate/mandate.

2014 games are already deep in development so lead platform is already established and likely the lead is no lead at all.  Also believe that resolution comparisons between X1 and PS4 amount to a pissing contest and for 90% of the buying public it will not matter one bit.

I have no doubt that Microsoft will work hard on the resolution issue. They will probably reach parity on that front eventually. That's too big of an issue to ignore, at least in terms of public perception.

The other side of the coin, however, is going to be how hard (or easy) it is to optimize for the PS4. The similarity of the architecture, both to PC and to one another, could mean that optimization is a process that is both quick and easy. "Lazy developers" is mostly a myth--time and money are usually the real factors. Well optimized releases for both the PS4 and XO should see the Playstation version with slightly improved performance and/or visuals.

That's only with games that are pushing the boundaries, though. A lot of games, probably most games, will occupy a middle-ground where they reach their best within the limits of the XO, so there are no more improvements to be found on the PS4 or PC.

Should be the opposite actually. The difference in power is only going to get worse over the course of the generation. Especially if PS4 dominates in sales.