I'm not out and out familiar with the Women In Prison genre, nor am I all that familiar with the work of Jack Hill. I came to this flick by way of a growing interest in Transgressive/Exploitation cinema of the 60's and 70's.
That being said, The Big Bird Cage is a strange animal of a flick. The trailer for the film comes off as a mean, angry, sadistic prison exploitation movie, when in actuality it's more light-hearted than it lets on. The plot is fairly simple, a band of revolutionaries, lead by Pam Grier and Sid Haig, plan to raid a women's prison/work camp in the hopes of boosting the morale of their troops (by getting the men some ladies) as well as starting a revolution (e.g. the storming of the Bastille in the French Rev.)
What follows is fairly entertaining fare involving bumbling overweight homosexual guards, a angry, tall, blonde, Amazon-like woman greased in chicken fat, and one of the best performances from Sid Haig this side of House of a Thousand Corpses. Though firmly rooted in the exploitation genre, this film feels more like an 80's action film than standard 70's exploitation fare (Thriller: A Cruel Picture, 2000 Maniacs, Ilsa, She-Wolf of the SS). I think it's because the film is more concerned with entertainment and crass humor than shock value and gore.
All in all the film feels like a long episode of the A-Team with a lot more nudity, mud wrestling, and female leads.