...depends, what kind of argument and what you understand by "winning an argument".
Mercury in Sagittarius could become really bothersome if you go in to details, they'll just want to have the last word at that point and they're willing to take the "long road" if you're not smart enough "to stop" - let them calm down and try to approach the situation from a different angle.
Mercury in Gemini can be very confusing if the conversation turns to argument - they'll derail the conversation getting in to all kind of topics till you see their point... and they might truly have a point regarding one of those "extra subjects" - but not the main subject on which that argument was based... they can say a lot of things in very short time - since this is their domain... so, would be wise to use other means than direct conversation or else would be impossible to win - even if you're right.
Mercury in Pisces can be evasive in arguments, if they can't make you see their point - they'd rather avoid you, not so keen in winning an argument if the evidence doesn't go with the way they feel about it. In their mind - their side is the right one and they hope you'd see their way at one point...
Mercury in Capricorn look for the practical side of the conversation - they tend to shut-in if it they get lost in details or see that the argument is going nowhere, they like to chose their words carefully and can't stand those that resort to verbal diarrhea.
Mercury in Virgo or quite good at winning arguments - and most of the time they're right, they're very good with details and can see holes in conversation, but also remember details witch the other party is missing - they're weak side can be related to conceptual conversation... that's one subject they're willing to let go if they can't win with a practical approach.
Mercury in Scorpio - tend to interrupt the discussion if their instinct doesn't fit with what you're saying... even if you're right it doesn't matter to them - once they set their mind on something - they become very violent in a conversation - especially if it turns in to an argument and I'd strongly recommend avoid getting in an argument with this kind... debates are simply not their thing and it rarely ends well... they will try to hurt you - using something they know about you against you.
Mercury in Aries tend to go with a blunt approach in arguments, might even result to insults...
...and so on - but i should mention that it's also related to their Sun Sign and the way Mercury is aspected... and that's where you'd notice a difference between people with Mercury in same sign.