This is a really good question and something with which, I am at least personally experienced with - in terms of having done recent research on the subject
Recently we (at Effect Digital, UK) moved office. I say recently, it was probably nearly a year ago now. Previously we had been using Moz Local, but were shocked to find that simple features like 'changing' or 'updating' our business address were not supported. The problem comes down to directory aggregators (the main offender being Central Index) and how they interact with various listing suppliers
When Moz Local failed to update our business address, we tried to contact a lot of directory-owners (and directory aggregators like Central Index) manually. Trust me when I say, the largest ones (like Central Index, which handle the majority of your directory listings across local newspaper sites - at least here in the UK) do not want to hear from you at all
We submitted contact forms, spent hours browsing to hidden contact URLs, even found a phone number for them - which rang for a minute, then forwarded to a separate disconnected number. These guys don't care about receiving updates from Moz and they don't care about your update requests. They don't even want to listen to you, for 2 minutes
The problem with Moz local, as a Moz rep told us - is that when they push data (from Moz's Local database, to the databases of aggregate listing handlers like Central Index), there is no legal agreement requiring the aggregator(s) to accept Moz's update(s). They will accept Moz Local's first set of data, but if you ever want to change anything substantial - that rapidly becomes a massive problem. Moz Local is a great way to take your first steps into local listings handling, but the solution isn't end-to-end, or rigorous enough for on-going usage
Yext is much better, from the sounds of it. Myself and another experienced colleague spent some hours on the phone to their support people who seemed qualified and able to handle our complex queries. They stated to us that, they have a more 'direct' agreement with listing aggregators which directly pushes their data over the top of everyone else's. That tells me that, either their solution works well or - if it didn't work, you'd have recourse to push them to get things sorted out. They take more responsibility and really try to make sure that their updates 'actually' end up live in aggregator databases (which is great)
We didn't end up using Yext because, as an SMB the pricing was pretty severe. We were told that Yell basically re-sell Yext's technology to smaller businesses and that we'd have better luck with Yell. Whilst Yell may be based on the same technology, the support is woefully inferior and I'd never recommend working with Yell. We had one rep visit us to answer technical questions. He knew none of the answers to our questions, knew nothing about SEO and actually had the tenacity to try and 'steer' us toward purchasing some crappy directory listing on Yell which wasn't at all what we wanted (or were interested in)
Moz is great when you're starting out, but because the 'deals' they have with data aggregators aren't 'forceful' enough, it's not a good on-going solution (Moz know this and said as much to us over the phone). It's still the best place for you to 'start' as the prices are great and it does function well, until more crucial data changes are required (at which point it falls flat on its face)
At that point you really should be going with Yext if you can afford Yext. The product is superior, the support is very strong (Moz's support is actually great too, but hindered by the product which is defective under some specific circumstances). In-between the cheap and cheerful Moz and the very expensive Yext, there's nothing good enough to fill the void (which sucks!)
You may have some luck manually adjusting some listings. But for the ones controlled by central databases which fire their data out to many directories, your only real option to have a reasonable shot at getting them changed - is assuredly Yext
