We have to catch Weedle and Sentret anyway for stardust and XP. Everyone evolves a lot of Furret, and those of you that aren’t into power leveling (e.g. being level 30+ and finding the diminishing returns of stardust investments after level 30 not so attractive) can get quite a few Beedrill too, if your biome is “buggy” enough.
Movesets
The only viable moveset for Furret is Quick Attack / Hyper Beam (the same as one of Raticate’s best movesets), while for Beedrill several movesets are good, just avoid Aerial Ace. Beedrill’s best moveset for general-purpose prestiging is Poison Jab / Sludge Bomb.
Typing
Furret is Normal, with Normal moves. So it usually receives and deals neutral damage. Notable exceptions: it resists Lick (e.g. Snorlax), it’s weak to Rock Smash (e.g. Rhydon) and it’s NVE against Rock (e.g. Rhydon, Tyranitar).
Beedrill is Bug/Poison, with its strongest moves being Poison. So its moves are neutral against pretty much everything typically found in gyms, except they are bad against Ground and Rock (so avoid using against Golem, Rhydon and Tyranitar, which anyway have their specific counters). It suffers Zen Headbutt (Snorlax, Blissey) and Psychic (Blissey) but it resists Dazzling Gleam (Blissey as well).
Stats
Beedrill, with its 169/150/130 stats (P = sqrt (D x S) / A = 0.83) is more attack-oriented, i.e. quite high DPS but not particularly resilient. The stats ratio is in the same range as Parasect, Venomoth, Sunflora and Machoke, and it’s still bulkier than Arcanine, Exeggutor, Charizard, Victreebel or Primeape at the same CP.
Furret, on the other hand, is quite tanky: 148/130/170 stats (P = sqrt (D x S) / A = 1.00) mean that it’s in the same range as Nidoqueen, Poliwrath, Bellossom and Muk and just slightly less tanky than Vaporeon at the same CP.
Performance
According to my CP efficiency calculator, here is the relative performance of Beedrill and Furret (in terms of combined time and revive efficiency) against some of the most common defenders gym sitters:
| Defender |  Furret QA/HB |  Beedrill PJ/SB | Benchmark | ||
|---|---|---|---|---|---|
 | Vaporeon | 58% | 62% |  | Parasect |
 | Snorlax | 72% | 70% |  | Poliwrath |
 | Dragonite (Hyper Beam or Dragon charge move) | 53% | 56% |  | Cloyster |
 | Flareon | 52% | (43%) |  | Magcargo |
 | Blissey (Hyper Beam or Dazzling Gleam) | (timeout) | 77% |  | Machamp |
These rankings are done with a 0%-70%-30% dodge setting, i.e. dodge only specials and more likely to dodge if using a non-Super-Effective fast move (because it doesn’t delay the “Defender used Charge Move” message).
In addition, Beedrill with X-Scissor is a great prestiger against 
Exeggutor with a Grass charge move, due to its 0.64x resistance to Grass and its 1.56x Super Effectiveness against Grass/Psychic.
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