That’s like asking which of your parents is responsible for your natural birth. Notice that John 3 mentions the new birth in the context of feminine or maternal imagery (the mother’s womb), whereas 1 Peter gives a masculine or paternal image (the "seed" of the word of God). The new birth is not water alone, nor the word alone, but the "washing of water with the word" (Eph 5:26). They should be united, not pitted against one another. In fact, Peter’s readers had been led by hearing the word to embrace new birth in baptism. Their new birth in baptism was the result of the word being implanted earlier—a spiritual "conception" in more than one sense.
Even if the images did conflict, this would not invalidate one or the other. After all, Scripture sometimes uses the same image for different aspects of divine truth. The Church is said to be built on the foundation of Christ (1 Cor 3:11), the apostles and prophets (Eph 2:20, cf. Rv 21:14), and Peter in particular (Mt 16:18). The image of a lion is applied to both the Lord and the devil. There is no reason why birth imagery should not be applied to both water and the word. As it is, though, the happy complementarity of the two images—a paternal and a maternal one—powerfully brings out both aspects of the new birth.