The primary similarities between Barca now and United around 2010 or so, is the obvious issues at board level that are resulting in poor recruitment and squad building.
We had SAF then to cover up the decline in the level of our squad and recruitment. Barca have Messi now who does the same.
They have bought a number of talented players in the last few years, but building up a coherent squad with complementary talents is more than just buying names. United struggled with this post-SAF as numerous transfers like Mata, ADM, Falcao, Schweinsteiger, Sanchez, etc. made clear. Only now after the club has overhauled how recruitment is done, including creating it's own proprietary database, and with a manager who has a genuine vision for how he wants United to play that aligns with the talent on hand does it genuinely feel like progress is being made.
Barca's issues, as I see it anyways, are that their recruitment doesn't seem to have much thought or process to it and the managerial appointments don't seem to have any common thread in the ethos and preferred style of each manager. The managers also don't match what you'd want with the recruitment, or vice versa. On top of that the mistakes they're making in the transfer market aren't failing on cheaper punts, but rather spending exorbitant amounts on big name players and talents, who struggle to adapt and need to be sold, but the club are unable to even get buyers for said player to recoup their investment. These are massive problems that have long-term impact.
The difference between Barca and Real's decline in squad quality in Ronaldo's later years there is that in that instance Madrid simply wasn't spending much at all, while they trimmed down the wage bill to keep their finances in order. They therefore had the financial muscle to invest quite a bit into the squad one year out, and the remaining spine was still quality enough in a bit of a down period for Barca and Atletico to capitalize and put themselves in the driver's seat for La Liga. Zidane's re-appointment as manager, a man who understands the club and proven he can manage the egos and win at the highest level at a major club like Real has also been a key factor.
Barca now having an aging squad with mega earners who they cannot offload easily, not without taking a significant financial hit, or even perhaps subsidizing the move themselves. On top of this the board situation is a mess, their managers have little power over a core of aging players who have gained internal influence and power due to the infighting and power vacuum at board level which complicates the process of rebuilding the team. Will they struggle as much as United did post-Ferguson? Odds are they won't, but Messi, as great as he is, has dropped off a bit and that means he can't cover up as much as he has, and that's something that is likely to only get exacerbated over the next couple of years, as well as natural declines for core players like Pique, Busquets, Suarez, Alba, etc.
They won't fall into the abyss, but I'd be surprised if they don't drop off in a major way over the next 2-3 years.