While some MC's have a bit of both, in general you can classify them into the following two categories:
- personality-based MC (the character has a defined personality)
- self-insert MC (the character lacks a personality and is a stand-in for the reader)
Visuals and Narrative
Basically everything you can see on the screen and the way writing is handled, such as point of view. The reason why I'm taking these together is because they overlap in visual novels.
As the MC does not represent the reader in this type, it's possible to show him/her alongside the other characters of the VN. This strengthens the idea of the MC having its own personality, which in turn helps the reader with their expectations of what type of MC and choices to expect. Of course, it's still possible to relate to the MC, so seeing the events from their point of view is equally valid. Since either (visual) point of view is possible, the choice depends on which one fits the creator's goals, story set-up and narrative better.
Most visual novels with self-insert characters are seen from first-person point of view. After all, this increases immersion as you don't see the self-insert, and it can be 'you'. While some games like western RPGs give you the option to customize your main character to enhance attachment, this isn't done as much in visual novels because of the detailed art and lesser budgets.
While both types might show their inner thoughts during the story, they serve a different purpose.
The thoughts of a personality-based MC are about the events in the story ('A werewolf infestation? Is the local witch behind it?'), but should also reflect his motives behind his actions ('My sense of justice does not allow me to walk away!'). As the reader needs the thoughts of the MC to understand him, it is important to not hide critical ones. If the MC takes an unexpected action without explaining himself, the reader won't understand him and will feel less connected with him. This also includes motives the reader cannot connect with, like a serial killer killing for fun.
In the case of a self-insert MC, his/her thoughts should either be about the events of the story or express thoughts the reader is likely having as well. Try to avoid thoughts that might not reflect those of the reader: if the MC is very sad at an event while the reader is not, the reader will feel more disconnected with the MC.
The kind of choices you encounter in the story.
With personality-based MCs, a choice can never be something which would be out of character. This includes matters where the reader is presented with choices about what the main character thinks of a situation. Since the MC has its own personality, he/she should already have an opinion based on their personality, so it makes no sense for a reader to decide.
It's still possible to give the reader a choice, but all options should be plausible courses of action for the MC. Examples of such choices are action choices (Stab the guy or blast him with magic?), order choices (visit the left room or right room first?), or moral dilemma's that are both valid options for the MC (kill the guy who killed your family or not?). Choices like these will create the feeling of being in control of the character - but not its mind - which we are also used to from games with this type of MC.
Contrary to personality-based MCs, for this type of MC all important decisions are up to the reader, as well as who to like and who to hang out with. You can even add choices that have little to do with the story, but give the reader the opportunity to role-play and grow closer to the self-insert. Longer stories can even tally how often certain responses are picked, and make the MC more angry, snarky or whatever relates to the answers best as a result. However, most VNs aren't long enough to utilize this effectively.
In short, the type of main character is dependent on which aspects fit the story better. Otome/bishoujo games benefit more from a self-insert MC, while some plot-heavy visual novels will probably want a MC with a predefined personality so the MC can take action on its own. Keep in mind what type of MC you want in your story, and model the visuals, narrative, thoughts and choices accordingly.