TMDB Vs TVDB

I want to begin the arduous process of fixing and organizing episode lists for Days Of Our Lives and General Hospital. I thought that trakt pulls data from TMDB. However, the data on Trakt matches the data on TVDB (which is more comphrehensive). I want to update the website that Trakt will pull from and don’t want to waste all this time if Trakt won’t sync with it. So which is it?

Days Of Our Lives is currently using TVDB and General Hospital is already using TMDB.
Pages usually have TMDB as the datasource, however, if data on TMDB is not updated, we keep pages on TVDB until the TMDB page matches, or has more content than their page.

You can see the datasource under the refresh button:
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So in this case, would you recommend me updating TVDB for Days Of Our Lives and TMDB for General Hospital?

Yes.
Since Days Of Our Lives still uses TVDB, you need to update that database to get the updates on Trakt. However, if you want to update TMDB to a point where the data there is better, we can migrate the show.
Pages that already use TMDB will continue in that datasource.