There are so many epic battles, and considering what your teams are (especially on your first time playing respective game) greatly changes how you feel about each battle. I remember my first battle with Brock being pretty epic. Same goes for Blue and Red, but I've also had some pretty epic matchups in the Battle Tower/ Battle Subway.
My all time most epic battle had to be when I went up against Lance in Heartgold. I had almost no items left, my team was fatigued, I was drastically underleveled, but I still pulled off a win. Starmie, Miltank, Jumpluff, Pidgeot, Typhlosion, and Onix. My team may have drastically changed since then, but they were victorious.