Tankai 说:
How would equipment and fighting style vary between those 3?
Those three what? Most of the time it would come down to personal choice, so equipment would be dictated more by what the person in question could afford rather than class or rank.
That's the problem. One of you is saying that it is determined by land, while the other suggests that it depends on how they're employed (i.e. longterm service, oath bound, contract work etc).
Man at arms or sergeant is determined by employment terms rather than wealth or land. It depends on how finicky you want to be. Technically, a Sergeant is anyone bound to serve (it's where it get's it's modern designation from) while a man at arms is any free man willing to bear arms. In real terms, you could be either depending on a number of factors, for example I've already mentioned the practice of entering one's offspring or butler on the list as a sergeant for monetary gain, a man at arms might find himself entered as a sergeant (and vice versa) for financial reasons too. A knight is exclusively determined by the granting of a knighthood, anything else is moot. It's not until higher in the nobility that you need land (Lordships and up).
I believe that in M&B this would include all current non-mercenary recruits as we nearly always hire troops to permanent positions. We don't deal with levying troops or hiring men-at-arms just for a campaign.
You wouldn't just hire them for a campaign necessarily. For example, your castle or town guard could well be men at arms, or you may hire a personal guard as men at arms (though it would be unusual). In this case it wouldn't so much be a case of the player recruiting them to join his party, more a case of offering them extra pay to accompany you in your wanderings rather than the (relatively) safe job of making sure nobody steals your village while you're gone.
In terms of M&B, most troops would be men at arms since you ask them to volunteer when you visit a village. You could split it the same way, with men at arms being the main recruits (from villages owned by other lords), while sergeants are only available from your own fief (since you can take those who have sworn an oath of fealty to you as their lord). In fact, one nice way to do it would be to have the sergeants require no wages, since technically their pay would already be taken into account from your fief outcome.