There are several different museums within the Hofburg complex, all of which are close to each…read moreother but require separate admissions. This was one of them. It seemed like it might be interesting, and online photos play up the 'crown jewels' type aspects. I bought tickets online. This was not one where you had a timed entry, so it had some flexibility. I don't recall if they required you to check backpacks, as we left ours at the hotel that day due to another associated museum's prohibition on them.
My verdict on this was that it was not as interesting as I'd hoped. Their breakdown is roughly: 20% crowns, swords, and jewels. 25% religious items like reliquaries. 50% robes (coronation, etc.). 5% miscellaneous. By far, the most common thing you'll see are robes / clothes. They did have a good audio guide (for a nominal extra charge). But if I'd known exactly what to expect, I don't think I'd have come here. It depends on what you are personally interested in, of course. However, given that most trips have a limited time budget, I think I'd have spent that time at some other museum / attraction instead.
We spent about an hour touring the whole place, which was not small.