First, there are general-use repositories that are not specific to materials modeling.
Zenodo. Like several other approaches, each project gets a permanent DOI associated with it, and new versions can be uploaded with the same unique parent DOI for the project and version-specific DOI. One major upside of Zenodo is that it is managed by CERN, which is likely to be around for a while. They also guarantee that should operations be ceased, they will transfer all data to a separate repository. Since the DOI is static but what it links to can be changed, this does not impact the findability of the data. One downside is that there is currently a 50 GB per-record file size limit, which may not be suitable for large-scale materials modeling.
Figshare. It operates in a very similar way with regards to have project- and version-specific DOIs, although they make no public claims about how they will ensure the longevity of the data. One major benefit of Figshare compared to Zenodo is that there are no project-specific file size limits (there is just a 5 TB limit on a per-file basis). Otherwise, the two platforms are very similar aside from user-interface.
Dryad. Also operates similarly as the above but specifically has partnered with various publishers, such as Wiley, RSC, and PLOS so there are some ease-of-use features if you're submitting a manuscript to one of those journals and wish to also deposit the data.
Of course, there are other field-agnostic platforms to host data, such as on GitHub or GitLab or Bit-bucket, but in my opinion these are not suitable for ensuring the longevity of data. The repositories can be deleted at any time, and there is no associated DOI.
Then there are topic-specific platforms. For materials modeling in particular, some big names are:
ioChem-BD. This platform is meant for hosting computational chemistry results. Each data repository gets a DOI. You can read more about it in this paper, although it is slightly outdated now. There is also this perspective on hosting data for catalysis research, written by the folks of ioChem-BD.
QCArchive. This is a repository fulfilling a similar niche as ioChem-BD, hosting data for computational chemistry simulations and making sure the data is findable while also providing interactive data visualizations. This is mainly meant for molecules. You can read more about the QCArchive in this paper.
NOMAD repository. This repository is also specifically suited for materials modeling (less so for computational chemistry). Once again, all projects get a DOI, and there is an API that can be used to interface with the data hosted on NOMAD. One subtle benefit of repositories like this is that they take care of issues you might not have thought of when hosting files for a given materials modeling code. For instance, it is against copyright to share VASP's pseudopotential files, but the NOMAD repository will automatically remove those (while storing the key information about what pseudopotentials you used) upon upload. You can read more about NOMAD in this paper.
Materials Cloud. This is a platform that is specific to materials modeling, but unlike ioChem-BD and NOMAD, it is not specifically focused on quantum-chemical calculations. You can read more about the Materials Cloud in this paper. One of the main distinguishing factors of the Materials Cloud is that it also focuses on making sure the workflows themselves are reproducible.
Catalysis-Hub. This is a data repository specific to quantum-chemical calculations related to catalysis and surface science. You can read more about Catalysis-Hub in this paper.
The main benefits of using a platform specific to computational chemistry or materials modeling is that they often make it easy to find other data or carry out meta-analyses, which are not practical on broader repositories like Zenodo or Figshare. In other words, they make your data more re-useable. They also are constructed to deal with common input/output file formats, oftentimes parsing the results automatically and displaying them in an intuitive way. This is also in contrast with more general data-hosting platforms, which effectively are just ways to host files as-is with some degree of longevity.
The main disadvantage in using a materials modeling-specific platform is that it may require more work to set up. You could, in principle, just dump all your files on a repository like Zenodo or Figshare. That doesn't mean they'll be easily findable and it's not necessarily advisable, but you could do it and it'd require little time on your part. In contrast, materials modeling-specific repositories are trying to make sure the data is consistently structured and readily accessible, so it will require a little bit more organizing time for the person uploading the data. Personally, I think that is a price worth paying.