I'm very late on the scene I realize, but as a follower of the Integral Yoga who started out as a Christian mystic, I might have something to contribute.
Thomas, you asked what it is that reincarnates. According to Sri Aurobindo and the Mother (his co-equal and spiritual partner, nee Mirra Alfassa) it is the psychic being that reincarnates. The psychic being is something like the soul. It is not the mind or emotions, however, and it is definitely not physical. I would paste a link, but apparently I am not allowed to do so in my first post. However, you can Google 'Sri Aurobindo. Psychic being' and it should help.
The hope in Sri Aurobindo and the Mother's (SA/M's) Yoga lies in their bringing nearer to us the actualization of the promise of glorification of the entire manifestation/creation. This was not completely realized in Christ's resurrection, as the resurrection represents an individual Supramentalization only (this is a high stage of Divinization. Here also a link would be useful, but meanwhile you can Google 'higher divinization stage of transformation', or search for it on www [dot] kheper [dot] net), whereas SA/M initiated a collective Supramentalization which was necessary for such glorification to be achieved by everyone.
Although Jesus was not less or more Divine than SA/M, he existed (i.e. in his embodied form) at an earlier stage in humanity's collective evolution, a stage at which collective Supramentalization was not possible even by the most Enlightened of beings (i.e. it was not God's Will at the time). Thus, as Jesus himself stated, he will return again, and he will return on the right hand side of Power. The 'right hand side of Power' statement also accords with SA/M's statement that Christ represented Divine Love, but both Power and Love will be needed, and experienced, for the Kingdom to come.
As should be clear by now, my view is that all the Avatars have been doing the same work. The work is to consecrate the world and speed up the process of evolution which will culminate in the coming of the Kingdom of God. Specifically, this work involves bringing down the higher, Divine consciousness to the lower, more carnal Earth/body, so that the distinction between the two -- that was necessary for the manifestation and for multiplicity -- can finally be erased. Thus, the difference between Christ and SA/M's message/work is not one of essence, but only of their relative positions on an evolutionary timeline. In other words, Christianity IS indeed an Integral Yoga, or at least one early realization of it.
Hope this was useful.
Cheers,
Komal
