Summary: Litchi is great app, well worth the money. Read on for the details.
As a UAS test pilot, I have flown just about every control app out there. And, of course, I fly the DJI apps half a dozen times per day.
DJI Go and Go 4 are the standard apps supplied from the manufacturer, so you have to have use them. DJI's app is always going to be the most up-to-date, and there are a lot of features that are simply not available in other apps (mostly related to UAV maintenance and calibration).
That being said, DJI's software is simply not very good. They have been very straightforward about their goals: They want to sell hardware. They don't want to maintain hardware, support customers, or develop more or better software than is absolutely necessary to meet that goal.
The DJI app tends to be buggy, with frequent poorly-tested releases. This last month, as they attempted to improve the on-screen video quality, DJI released a version of their app every few days because it failed to run on many devices, reporting "poor connection" or "lost connection" and displaying really poor video. For times like these, it is essential to have a backup app that you can use to verify that you are looking at a software problem and not a vehicle problem.
Also, there are a lot of features in Litchi that are not available in the DJI app. For example, if you have a new vehicle and you want to check out the electronics without going through the registration process (which essentially makes it a used vehicle), you can power it up and check it out in Litchi. You can not do that with the DJI app.
Also, Litchi gives you the ability to plan a flight, load the flight into your UAV and then execute it. This is wonderful if you are planning out a complex shot for TV, film or construction progress. You can store the complete flight instructions and execute them over and over, enabling you to fly the same exact course on a different day, in a different season, or simply repeat it because the talent wasn't doing what they were supposed to do.
Even more remarkable is the ability to plan an entire shot on your desktop computer. Smartphones are wonderful for their portability, but drawing with your finger on a tiny screen is no match for being able to use your mouse with a big desktop monitor. Flight plans are stored in the cloud and made automatically available to your handheld device when you log in, so all you need to do is load and fly. I save hours of on-site time by planning a series of flights before I arrive on-scene. When I get there, I make a few adjustments as necessary and then fly the course.
Litchi also makes a number of the latest intelligent flight modes available on older craft, giving the Phantom 3, for example, follow-me, panorama, orbit and other capabilities.
Compared to other apps, Litchi is kind of expensive at $25. But I think it pays for itself every time I use it.