Models -

In your own opinion, is it better for a model to develop a personal brand OR to be as versatile as possible?

I don't think either of these two approaches in any way excludes the other.

Branding isn't so much about defining an image as it is about refining a connectivity between venues in which one appears. So for instance, a profile here connects to a website with both attached to an Instagram account, and so on — the idea being that people visiting one portal as an access point are channeled to other places where you appear, rather than exiting to outside venues where you do not have a presence. THAT'S establishing a personal brand.

In contrast, a person could have a consistent presence or area of specialization that is presented across all venues in which they make themselves apparent; or, they could manifest a particular specialization at each of their portals; or they could present mixed weightings, with artistic or product placement or clothing appearing foremost at any one, with other aspects secondary for each. So establishing a personal brand could encompass any of those approaches.

Probably the best approach is to "mix it up" so that people find something a little different as they navigate between each branded link you provide, with different interest groups being drawn in to each portal but all in the end navigating through a full presentation of your various specializations and talents. The key to this is, once again, establishing your branding as an internal connectivity that brings people between YOUR links, rather than dropping the ball and having them leave to somewhere from which they'll never return to your venues.

In philosophic terms, this is called "differential repetition" and the idea is that people encounter new things as they look around, but without leaving the connection to what YOU are doing. That keeps their interest focussed upon what YOU are doing.

Just a suggestion!

Not familiar with any model promoting a brand. They promote themselves, and if they have an agent, the agent promotes them. Never encountered that, in my almost 40 yrs, of commercial work.