Pet battles have gotten a lot more sophisticated from the beginning days. Where when it first began everyone just used most damaging attack as soon as possible, now there is strategy. Reflect changes certainly made it a lot more tactical where just having big hitters doesn't auto win, although still is an advantage.
Players these days swap pets, change up their moves, combine moves for extra damage or for mitigation. It has gotten a lot more interesting now. Most players try to play different random pets to make it interesting, so don't be afraid to do so as well. You are not going to run into elite teams all the time.
Having said that there are some very strong, and cheesy teams out there. Multiple speed FFF's or multiple speed basilisks are super cheesy and cheap. First one doesn't really have good counters short of them screwing up and throwing all their 1800+ hits against your magical pets (reduced to roughly 400 due to magical racial). Second one is stupidly OP too in most scenarios.
Another strong team you'll run into once in a while is blizzard based. Usually snowman + kun lai runt. Unless you can change weather on them, preferably into arcane winds expect to get stunned a lot.
A good combination to try, has worked well for me (unless I get too many misses) is Curse of Doom amplified. Done right, will damage your opposition for roughly 1100 and heal you back for the amount. Undead do well right now since there are really no critters in the game... they all suck.
Hope this helps.