Sri ganesh_mourthy,
I know very little about kucipuDi - what I know is that like kathak in NI, kucipuDi is a dance form where the practitioners went from place to place singing and dancing the praises of krishNa, and enacting his divine lIlAs. It is named after the village in AP where generations of brAhmin boys learnt the art form and lived off their earnings by retelling these stories arranged as elaborate nATya productions. Only boys and men were allowed to learn this form, and Smt. Yamini Krishnamurthy was the first woman to learn this art form and perform it on stage. So, while bharatanATyam evolved from temple services (nATya sEvA), kucipuDi evolved from a story-telling tradition. bharatanATyam was, and remains to this day, predominantly a solo performance style, with a mArgam laid out by the quartette, while kucipuDi was predominantly a 'dance-drama' type of art form, and a solo mArgam had to be evolved when people began to give solo performances very recently in the 20th century (the reverse happened with bharatanATyam, with the kalAkSEtra leading the way in choreographing dramas). Another difference between bharatanATyam and kucipuDi is that while the language of the songs for bharatanATyam included sanskrit, telugu, kannaDA and marAThi in addition to tamizh (even in the days of yore), songs for kucipuDi are mainly in telugu or sanskrit. Very recently, Sri OVK's tamizh compositions have been choreographed in kucipuDi.
Technique-wise (now, I am on more of a slippery slope here!:)), I think kucipuDi is way faster than bharatanATyam, and emphasis on 'araimanDi' is very little in the nritta portion. tIrmAnams are very different, and there seem to be more upper body (waist) movements. In choreographing lyrics, the difference from bharatanATyam becomes very evident - bharatanATyam choreography is padArtha - meaning, each word of the sAhitya is matched by a corresponding action, while in kucipuDi it is vAkyArtha - with the actions bringing out the general import of the sAhitya. For example, take the phrase 'nI ingE vA' - in bharatanATyam, the actions will match 'you','here', and 'come' in that order, while it is perfectly acceptable in kucipuDi to mime 'you come here'. Finally, items like tarangam are unique to the kucipuDi style where the dancer dances on a plate.
If others (like apsara/avnipriya) can add some more it will be awesome!
Here is a jatisvaram in kucipuDi style:
http://www.youtube.com/watch?v=DbWXTnc4ooo
See the tIramAnam between approximately 1:38 and 1:43.
And here is the famous rAgamAlika jatisvaram of the tanjAvUr quartette in bharatanATyam style:
http://www.youtube.com/watch?v=t5vNE-4o ... re=related
Watch some of the tIrmAnams (between approximately 1:15 and 1:20, and 4:31 and 4:36 for example) to see the contrast.