No it's not.
As I said, it's who knows how to use them best, and by that I do not mean the effects, as you say, they are fixed for each spell. I mean by which spell to use when. Someone with vast amounts of spells might get carried away and cast spells that make them tired very quickly meaning the other person, with just a dozen or so spells, could take advantage of the situation.
The one who has the most spells may well have a huge advantage but only if they know how/when to use them properly. Someone with a vast quantity of spells who does not know how to use them best will probably find having so many options a hindrance rather than a help.
That's a lot like saying, "Well, yeah, your opponents are going to have swords, daggers, and crossbows and you're just going to have a club—but they might be really stupid and not know how to use them, so you should be fine!"
