We struggle to effectively search old tickets in Hubspot.
1. There is the global search. It does offer full text search. However, the provided results are often not user friendly. Often you get many duplicate results. Example where the first 8-10 results are all the same record:
2. There is the search from the tickets list view. However, this search does not use the titles of the ticket and cannot search through properties, emails, notes etc.
3. There is the search on the record page. Here we often don't get results even if the type exactly the wording as in the email.
We have multiple people coming from Zendesk to Hubspot and they are of the opinion that Zendesk makes it much easier to find old records again. Maybe you can compare the two solutions.