The Big Three are overplayed, so people know more or less what to expect.  A
good trainer willing to spend a little time and money on his deck can easily
mow them down.  Below is a list of easily exploitable weaknesses that the Big
Three decks have.

Haymaker:  I have had an enormous amount of success aganist this with a
poison/elec deck. If you want the full decklist, you can e-mail me, I'll send
it to you.  It contains 4 Electabuzz, 2 Venomoth, 2 Jolteon, and 2 of the 
ever-so-versatile Scyther.  Buzz and Jolteon have a chance to do 40 and 80
damage respectively for a very minimal amount of energy, and Scyther and
Venomoth are resistant to Hitmo.  Just keep your pokemon from getting Gusted
off your bench to face pokemon that they have a weakness to, and if you do,
heal em with Pokemon center.

Raindance:  I used the same poison/elec against 2 basic Raindance and 2
variations.  Only one of them managed to beat me.  Blastoise tends to die
rather quickly when you gust one out against Electabuzz.  Scyther counters
Gyarados.  Articuno is a weak joke.  Lapras is an even weaker joke.

Stall decks:  In this case, it is more the trainer than the Pokemon.  Not too
many people I know play this deck, but I managed to track down my cousin's
neigbor in Camden and, after asking and begging several times, I battled and
conquered him.  He played a Fossil variation where Fossil Haunter stalled
with its amazing power, and every time I damaged him, he used Alakazam to
damage swap it away.  However, he failed to draw me out.  I resisted the urge
to play Bills and maintained a large hand so the kid couldn't use his
Imposters to any degree of advantage.  Eventually, he drew himself out(he
went first).  However, this was only one deck, and probably not a good test
set.