Quizlet is based on a 'flashcards' model. The teacher or the student can create a 'study stack' which the student can use independently to learn terminology or for self-testing.
There's a huge number of study stacks already created and posted on the site which you can use if you don't want to create your own.
It's the 'Quizlet Live' feature which is really useful for a class quiz. Questions are drawn from existing study stacks so there is no extra set-up if you want to run a quiz. It can be done almost immediately. It really only works as a class activity, though. You can't really set it for homework.
Students work in teams, which can be randomly set. It's competitive between teams and very enjoyable, especially as a lesson starter. You do need at least 6 students to be able to play, though. Students play on their own devices and there is a mobile app which is pretty good.
It does integrate with Google Classroom but it won't pull in the scores to Classroom. In fact, it gives you very little information on student performance and isn't particularly useful for analysis. You can subscribe as a Quizlet teacher (for a fee) and that will give you some more information - but not a huge amount.
Quizizz is attractively designed and is fun for students to use.
Like Quizlet, it works on students' own devices and there is a mobile app available.
The key difference with Quizlet is that students work individually rather than in groups. That means that quizzes can be set either as a class activity or to be done outside class. In both cases, you can have a 'live' league table which introduces a fun competitive element (though you can hide this feature if you prefer). There's no limit to the number of participants.
It integrates well with Google Classroom and quizzes can be scheduled there very easily - though it won't draw the marks straight in to GC. The integration is a new feature and they promise it will develop soon - so maybe the automatic recording of student results will be part of that.
You do have to set up quizzes in advance - although there are lots in the library you could use 'off the shelf' as appropriate. It's also very easy to 'teleport' questions from existing quizzes into your own.
Results are reported in lots of clear detail and they would be very useful for analysing areas of strength or weakness.
Students work individually on Quizalize. They can use their own laptops but there is no mobile app yet. Quizzes can be played in class or as a homework activity.
It looks attractive and it's easy to set up a quiz, which has to be done in advance. It's also possible to import Quizlet study stacks to speed up this process.
There's a good number of quizzes already in the library, though there is a charge for some of them. (Usually about 79p).
It does integrate with Google Classroom, though, like the others, it won't yet put students' results straight into the assignment. You can subscribe to the 'Teachers' Plan' (prices start at £4 per month) which removes the limit on the number of classes you can manage.
The strength of this tool really lies in the the reporting of results, which is very detailed and easy to read.
They also have a feature called 'Mastery Dashboards' which align quizzes to a public curriculum. At the moment, the only UK curriculum is the National Curriculum for Maths but this feature is still in Beta and it will develop. They plan to allow you to create your own curriculum in the near future.
We don't always think of using Google Forms as a quiz tool but, like everything Google, it is beautifully designed and very versatile.
It's not ideal for quick quizzes in class and it doesn't have any of the 'fun', competitive elements like league tables or funny memes if you get a question right.
However, it's definitely the best if you want to integrate lots of information such as Youtube clips or other documents into your quiz.
It also offers the widest range of question type.
It also allows you to create very sophisticated, branching quizzes where subsequent questions are dependent on the answers to earlier questions. That gives it lots of potential as a diagnostic tool.
Needless to say, it integrates closely with Google Classroom and it's now possible to import the marks automatically into Classroom and, therefore, into your mark book. This video shows you how to do that.