Did anyone use both? And your opinion? How often do they make mistakes?
Grammarly is software for fixing grammar, punctuation, and spelling mistakes. It also will suggest rewording and stylistic changes
It's generally pretty good at what it does. It's not perfect, it makes both errors (in which it suggests changing something that is correct) and omissions (in which it misses something wrong), but it is a lot better than the spell-checking and grammar software of yesteryear.
It is primarily aimed at native speakers, but it will do its best with text from non-native speakers. I would recommend that everyone use a spelling checker for text that is intended for others. But don't be afraid of saying no to Grammarly.
In this answer, so far, it has corrected a mistake in hyphenation, and several typos. It also identified a problem with "don't be afraid of saying no", but its solution to the problem was incorrect (it suggests removing the double negative, in fact I should put quotes around "no"). It is also quixotically keen on commas after introductory adverbials, but it dislikes commas after coordinating "and" if the subject in the second clause is omitted.
One fact about Grammarly is that it can have settings. It can be set to British English, for example. ChatGPT can also work in British English, but it has to be asked, and it doesn't remember your preferences.
ChatGTP is a completely different kettle of fish.
It doesn't check grammar. It generates text in response to a question. It won't identify errors in spelling or punctuation. It will try to respond to your text and is intended to be able to work with questions that contain errors in Grammar.
It has been trained on a wide variety of sources. This enables it to respond to questions about grammar, and it normally does quite well! However it doesn't know anything. Like many native speakers, it doesn't understand its own grammar rules. It will spout grammar facts from its training, but those fact can be confused or contradictory.
For example, you can ask it if an adjective is an adjunct. There is a difference in terminology used by linguists, so the real answer is "You should get your definitions clear" Some linguists consider "adjuncts" to be elements of the clause structure, and not elements of the phrase structure (and hence adjectives are not adjuncts) But others use "noun adjunct", for example (and hence attributive adjective are adjuncts).
Grammarly doesn't care about names. It will try to identify incorrect use of adjectives, but it doesn't care if they are adjuncts or not.
ChatGPT will have an opinion, but since there is genuine variation in the definition, and it is trained on both it is likely to pick a definition, but then, if challenged, it will change its mind.
ChatGPT is not designed as a grammar checker, it doesn't check grammar.
What it can do is rewrite something for you. This is a much higher level of AI, it is using its model to create a text that has the same meaning but phrased differently. It isn't spotting and correcting mistakes, it is taking your words, and trying to express them more clearly.
Again, it usually does a pretty good job of this. However, the problem can arise when your original text is unclear, as the AI may "fix" it to mean something different than what you intended.
In the above text ChatGPT suggests one change, using a semicolon instead of a full stop. It's much less convenient to use ChatGPT for proofreading. You need to copy the text into the AI (and it has limits on how much it can handle) Grammarly runs transparently in your browser.
Moreover, as it is rewriting your text, you loose part of your individual expression. I can usually tell on ELL who has written an answer by their style. Michael, Jeff, Kate, Fumble, they all have an ineffable quality to their writing - their individual voice. AI would reduce this variation.
Ultimately this question is like asking "Is a motorcar good for digging holes compared to other tools like a spade". A spade is a good tool, though not perfect, and it has its limitations. A motorcar does something completely different.
I suggest you experiment with both. They are both powerful, sophisticated, and subtle. But use them wisely, and don't assume that they always give the best advice. Your ultimate aim is to develop your own voice.