1. https://news.ycombinator.com/item?id=21998632
As a reader, I'll give a lot more weight to something with details attached. A medium-detailed blogpost about why a small company is working with you and what that gave them, or something I can see/confirm being used in practice, is worth a lot more than a meaningless Fortune 500/FAANG logo on the front page where I'll assume that "ok, one person with a corporate mail address signed up for that product, or maybe one small team uses it".
If you use a logo without permission especially from a larger corp, you might run into legal issues or maybe even jeopardize a deal that is in the making with your company.
Some public record clearly stating that a company X is using you can help to migitate the risk (public Job posting, article, webinar, etc.)
And of course always take down the logo if someone from the company is complaining. The very best is always to get permission from the companies marketing, business, legal or sometimes even hiring department, depending on the market you are in. Would recommend to go for case studies highlighting them and their solution and then get the logo that way.
Hope I could help a bit...
The last company for which I worked usually added a clause stipulating that they could not be identified as a customer without explicit permission.