Well, it won a Regionals, can't say that much bad things about it. And no, it's not like Kricketune.
Beedrill is a decent card overall. 110 HP is a bit low for a Stage 2 when compared to the now standard 130 HP, +30 Weakness to Fire leaves it open to Magmotar most of the time, and it has no Resistance or Retreat Cost. Band Attack is the main reason to run Beedrill; for 1 Grass Energy, he will do 30x the number of Beedrill you have in play. This means you can do a minimum of 30, or a maximum of 120, which is a very good ratio for 1 Energy. Twineedle should probably never be used unless you're desperate; it is overpriced at 3 Colorless Energy and does 50x the number of heads (only 2 coin flips), making it very unreliable.
Modified: 7.5/10 (Well, it did win a Regionals, but it's still weak to Magmotar, which is one of the dominant decks out there)
Limited - 2/10 (Unless you draft a heck of a lot of Weedle, Kakuna, and Beedrill, you're never gonna get him out)
Unlimited - 1/10 (No real use here, there are better Pokemon)