How specific is your NICHE?

How specific is your niche and how much does it matter? For example, if you had a website that sold cups, how specific would your product list be? Selling cups is already a specific niche, but I can see that it deepens.

1. A general website of cups that sells ceramic, glass and theft cups with or without designs on them.

2. A ceramic mug website that only sells ceramic mugs with or without designs on them.

3. A ceramic mug website that only sells ceramic mugs with a specific set of designs, maybe just mustache stickers. (Oh, they're out there)
http://mustachemug.com/

In terms of profits, traffic and growth, how do these problems affect a website? Obviously there are benefits for either of them; A general website of cups could sell a wider range of products, perhaps even more than just cups, such as:

https://society6.com/mugs
SEMrush

Although with a very specific niche, such as a website that only sells ceramic mugs with whisker designs, their product list will be smaller, but they can crowd the market for people who want … errr … mugs with mustaches in them.

I would like to hear from you guys. What you think about this? How specific should our niche be?