Ghostery breaks so much stuff, I don't know how people can bother. I've found that Privacy Badger does a great job of blocking third-party tools in a way that rarely breaks anything - in which case it's easy to turn off.
Ghostery developer here. As someone else pointed out, it's usually analytics tied to certain events like button presses, ads that trigger the main content to load after it shows, or fonts loaded from a 3rd party like Adobe that break sites. When we block the javascript and the developer didn't use a try/catch around that analytics/ad call, it breaks.
Most of the time there's no way around that breakage except by allowing the script (unless you use surrogates). So if Ghostery breaks the page and another blocker doesn't, usually that means that the other blocker is not blocking that script.
Adblock Plus lists, for example, contain extensive exceptions to allow scripts/ads on certain broken sites. This improves usability greatly and is a big reason some people are happy with ABP and not Ghostery. This isn't done in the most transparent way though, which leads to people unjustly accusing them of accepting money to allow ads when they find out about these exceptions. (This has nothing to do with the non-intrusive ads feature, which is a separate issue)
I've been using Ghostery for a year or so now (and prefer its UI over μBlock), and I've had minimal issues. If something breaks, I paste the URL in am incognito window. If it works there, I know it's a Ghostery issue.
I've been using Privacy Badger for 6 months and I can't recommend it enough for non-technical people (or technical people that don't want to debug websites all day long).
The one problem I've found is that certain services that use a bookmark/iframe combo (instapaper, for instance), create problems because you want to whitelist instapaper, but aren't given a chance. For that, I recently found: https://tsibley.net/provoke-the-privacy-badger/
But it's based on AdBlock code. I started using uBlock instead of AdBlock Plus in order to save some resources. It seems that adding Privacy Badger would introduce that performance hit to the equation again.
The only really noticeable impact I've seen is that it blocks Disqus, which too many people seem to use for comments. That's usually not a problem, and I can always disable it in the rare cases where I really want to comment on something. What sites are breaking for you?
It's been a long time since I used Ghostery, but the most common problem were JS trigger events from clicking a button that didn't fire. It made it a bit of a pain to debug.
That and Ad Muncher for Windows.