It’s a new feature, but not an empty data set. MusicBrainz’ genre support is basically a server side whitelist over the folksonomy tags feature that has been around for years, so there is plenty of data already.
The reason this is currently not working reliable is that it currently fetches only genres / folksonomy tags on the release level due to a server side bug. See Folksonomy tags no longer work as of v2.0.0 for details.
The difference is that they use different data sources. The built-in feature in Picard uses MusicBrainz, the plugins external data sources. There is no general rule what to use, but I can give you my opinion:
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Picard built-in Genre / Folksonomy Tags support: This would be my first choice, especially with the recent implementation of genre tags on MB server. So I hope the aforementioned bug gets fixed soon since it makes this feature less useful right now.
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Last.fm genre: This is very similar to the built-in support, but uses folksonomy tags from last.fm instead. Last.fm has been around for a long time and it’s tags are very comprehensive. So you usually get comprehensive results. But you need to keep an eye on the results since there are also non-genre tags you might want to blacklist.
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Wikidata genre: Regarding the data quality I think this is a great source. It’s more structured then the open folksonomy tag approach of Last.fm, so you usually get only actual relevant results. But the downside is that querying this data involves a lot of additional API calls, so enabling this plugin slows down Picard’s loading of albums noticable.
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AcousticBrainz: As the name suggests this uses AcousticBrainz as a source, which gets it’s genre data from analysis of the audio. An interesting approach, but IMHO the results are not too useful in practice.