No offense to everyone in the thread but most arguments I've read here are out of scope for Berry Juice's brokeness (ie. defensive Pokemon, Recycle, etc) or are severely underestimating of the effects being shot up to full HP after a boost.
In little cup, the only real ways to beat down set-up Pokemon is through very fast Scarfers, priority or (new to gen 5...) immensely bulky Eviolite users. If I'm Omanyte, I use Shell Smash, I'm taking a hit, probably losing 60-70% at the very least. I'm now low enough for almost anything that isn't relying on a weak Quick Attack or Ice Shard to KO me but I can sweep if you don't have anything to take the hit or priority.
Now imagine what it's like when all of those methods are made useless. If you don't OHKO a Pokemon, you automatically 3-4HKO it. There are no 2HKOes anymore. Your Frillish can't even reliably take out Omanyte with Surf (has something like a 6.25% to KO) and it can 2HKO you easily. I'll give you even scarier examples, lets start with Bagon. It's scary to think about how only crazy powerful Pokemon such as Flight Gem boosted Acrobatics Gligar can even come close to OHKOing Bagon, meaning you otherwise let Bagon get 2 Dragon Dances. Dratini has similar bulk on the special side and has access to fucking ExtremeSpeed.....not even priority can help after 2 Dragon Dances. How about not being able to do anything with Frillish while Misdreavus sets up an absolutely free Nasty Plot while retaining it's 100% HP. Have you ever tried to OHKO Misdreavus...? Even Stunky loses because you can 2HKO him with Shadow Ball -> HP Fighting and avoid Berry Juice or straight up OHKO him with Hidden Power Ground (why it's not as useful on defensive Pokemon).
I have yet to reveal the most devastating strategy for use with Berry Juice too, if you aren't familiar with it. I'm sure someone will come up with a list of calcs of relevant set up Pokemon that are OHKOed. Then you go on the ladder, see an Abra.
"What's this Abra going to do...."
Turn 1 Reflect, Turn 2 Light Screen. Turn 3 go to Bagon, Turn 4 "LOL didn't you see my Bronzor" while he sets up a DD. Turn 5 you HP Ice and realize that it 5HKOes, get gets another DD. Turn 6 you HP Ice again, he's now at full HP and +3. If you use Berry Juice you get OHKOed 100% of the time right here, if you use Eviolite you have a good chance to survive so he Dragon Dances again and with at worst ~60% of his HP left it can now outpace and OHKO almost every Pokemon in the metagame with Fire Fang, Dragon Claw, and <filler/Substitute> while only being touched by Ice Shards that still don't even KO.
Now imagine Dratini who takes even less from HP Ice and can't be stopped by priority.
Another thing that is not being considered is the use of Encore users. You can't always choose whether or not you get the right Pokemon out to OHKO another Pokemon. (ehem) Back in the day, you go to Wynaut or even just sacrifice something then bam you have Krabby with +2Atk+2Speed and still full HP....and you win just like that.
tl;dr stop underestimating Berry Juice.