Is one better than the other? Does one have features that the other doesn't?
The ITA Matrix software was developed by MIT engineers. ITA was then purchased by Google, and used to power Google Flights (as well as other non-google flight search engines). Quoting from the ITA website:
In the mid-nineties, a group of MIT computer scientists took aim at a complex computing challenge that had plagued the travel industry for three decades: how to quickly, consistently and accurately identify the best available airfares without relying on high-cost, low-efficiency mainframe computers. The results of their work was a revolutionary airfare pricing & shopping engine called QPX. The beta version of QPX was first introduced to the public in November 1999, and Orbitz became the first customer in 2001.
On April 12, 2011, Google acquired ITA Software, and shortly thereafter launched Google Flight Search, an incredibly fast and easy way to search and plan travel. So the Matrix isn't better nor worse than Google flights, since the former relies on the latter when looking for flights. It's just a matter of using one tool versus the other. Personally I stick with the Matrix because I've grown fond of the interface.
The main feature difference would be that you can purchase some plane tickets via Google Flights, whereas the Matrix itself does not allow you to do so. Moreover, the ITA Matrix seems to give you many more search options than Google Flights. Finally, Google Flights, being a Google product, will integrate with other Google products whereas the "pure" Matrix might not always.
I’m retited. Hv no dog in this hunt. I used ITA Matrix professionally & personnaly for more than a decade. It was & still is superior because it catches without fail all airlines minus Southwest. Misses no detail on what flight is avail for you & always finds the rock bottom eheapest as well as allothers. Most helpful is it offers way more categories to include in your search than others do, so you spin your wheels less getting to what works for you.
Ex: If I can only depart after 3 PM, will not consider more than 1 stop or only a nonstop, and ned to get in by a certain time on my return flighht, all that and more is there to select on 1st inquiry so you don’t hv to wade through lists of flights that will not work for you. Way more effiscient.
Google Flights does not offer as many categoreis so a bit less helpful 5us comes in 2nd among air search engines, but since using the same software, finds all/more flights than other search engines and does it fast. They are both superior to others. My knowlegde is based on booking decades of travel as part of a job in Congress, many last second flights, many long complicated foreign trips, et al. Hope this helps you.
The main difference is you can not book flights directly from ITA Matrix software. Since it's independent from a booking system it can give unbiased results, hence sometimes cheaper flights. I suspect Google Flights is using the ITA Matrix engine and then adding their booking system to it.
You can, however, take results from the ITA Matrix software and book it yourself. Here's how to do it.