So far (7 gyms in) I've had a few hard battles.
The second battle with my Rival (whom I named Steve) at Azalea Town came down to the wire, with his Lv18 Croconaw and my Lv14 Quilava both at a sliver of HP. If I hadn't used Quick Attack, I probably would have lost.
The battle at the Radio Observation Deck with the last Rocket executive was pretty close too. His Houndoom had managed to knock out 3 of my 5 Pokemon, until I knocked him out with Typhlosion. Kadabra was still waiting in the wings, but I don't think there was much it could have done against a dark-type like Houndoom, even with Miracle Eye activated.
On the other hand my easiest battle (and the only Gym I beat without any serious trouble) was definitely Morty. Kadabra's Psybeam made short work of Gastly, Haunter, Gengar and Haunter. You bet I felt like a million bucks after that was over. :)