Both. You'd definitely have an advantage (mastery in any pertinent martial skill is going to confer at least some advantage) but the role of swords in medieval warfare is generally overrated. The reason they figure prominently in our imagination is that they were prestigious and expensive weapons, so they are associated with the aristocracy and are represented in art more than their fair share. They are also much more prevalent by the time of the Renaissance, and we tend to mistakenly back-date 16th Century technology to the medieval period because Renaissance artists also did exactly that.
Evidence from early medieval Frankish burials shows that axes and spears were the most common hand-held medieval weapons, and even amongst swords, the classic medieval straight, double-edged cruciform guard knightly sword was comparatively rare compared to short swords and sax-type weapons which our modern sensibilities would be inclined to classify as daggers.
For almost all types of soldier, the sword was not a primary weapon of battle. Knights charged with the lance, infantry defended with the spear, and attacked with axes, which had the advantage that they could be swung or thrown. The sword was the fall-back weapon, most useful in the general melee after order had broken down and primary weapons were exhausted or broken. If the battle went well, you might never even have cause to draw your sword.
Longer swords increased in prominence toward the end of the high middle ages as improvements in metallurgy mitigated the costs associated with the weapon. A purchase order from 1295 on behalf of Philip the Fair documents the purchase of 13,495 spear and lance heads, 1,989 axes, and 14,599 swords and daggers. That unfortunately doesn't help us understand what proportion of those swords were long swords, and which were simpler and shorter weapons like falchions and daggers. Given the comparative expense, we should probably assume that most were shorter weapons, but it is still reasonable to suggest that heavy swords were at least competing with axes by this time in armouries. The same purchase order also called for over 600,000 crossbow quarrels, just to give you a sense of proportion of which weapons were most heavily used.
But since you describe yourself as a master swordsman, I'm actually going to assume that you are neither from the knightly class, nor a common infantryman. By end of the middle ages, the importance of the sword in personal combat was much higher than on the battlefield, and sword master was a recognized profession. It was not as military in nature as you might think. Swordplay was well-established as the civilian martial art of choice by the end of the middle ages, and fencing masters placed heavy emphasis on swords in various styles (sword, back sword, two-handed sword, and rapier by the late 1500s). If we assume that you are a master swordsman of the late middle ages or early Renaissance, you are probably trained in a number of sword fighting styles with an emphasis on single combat such as might be called for in duels, judicial combats (wager of battle), or simple self-defence in bad neighbourhoods.
Such skills could obviously serve you well on the battlefield once order broke down, but the battlefield was not a duel or a street fight, and the odds were that you had a completely different weapon in hand when the battle began. If it got to the point where you had to draw your sword, the day might be going seriously sideways for you.
War in the Middle Ages, Philippe Contamine (English translation by Michael Jones)
The English Master of Arms, J.D. Aylward