It is a relief to drop the liturgical re-education necessary to prevent the mother handing the baby over to the Godmother for the ceremony. The "exorcism" in the newer rite is as bland as possible in contrast to the older rite's determined exorcisms, warning the devil in the name of Christ to get out and stay out.
The "come on now, you renew your baptismal promises" element of the new rite was criticised by Cardinal Ratzinger in "Principles of Catholic Theology" (page 42, footnote) when he lamented the disappearance of the idea of representation. As he said,
the statements now designated as acts of remembrance have no inner relationship with the baptism of the child that is presently taking place. [...]The other prayers - with the salt, the sign of the cross, the anointing with Chrism, the clothing with the white garment and the handing-on of the candle all seem so much more direct and comprehensible. They can all, of course, be said in English according to the rules in force in 1962.
the whole raison d'être for the baptism of children has been nullified; there is no longer any justification for it. Granted, the rite in its new form has gained in immediate comprehensibility - but at what a price!
The rite then finishes with a simple "Go in peace N. and the Lord be with you." No blessing of the father, the mother, and uncle Tom Cobbley and all while everyone is standing there wilting. The blessing of a Mother after childbirth is a separate rite - beautiful in itself and without any hint of the sometimes-alleged "purification after childbirth".
I was pondering all this and questioning in my own mind about a teeny scruple. Don't the parents have to ask for it? So I turned back to Summorum Pontificum:
9 §1. The pastor, having attentively examined all aspects, may also grant permission to use the earlier ritual for the administration of the Sacraments of Baptism, Marriage, Penance, and the Anointing of the Sick, if the good of souls would seem to require it.OK, with my arm twisted up behind my back like that, I'll grant myself permission.