The liturgies for Palm Sunday which are in use, de jure or de facto, in the 'Roman Rite' of the Latin Church are:
(1) S Pius V
(2) Pius XII (1955)
(3) The Novus Ordo.
I am not going to say much about (3). I am going to explain why, in my opinion, (2) is as bad as, if not worse than, (3), and I will explain what was lost when (1) was displaced by (2).
A spin-off from this is: we need to understand that 'the Council' is not the problem; Hannibal Bugnini was put in place by Pius XII, and the mayhem which the pair of them created in 1955 was just the first stage of the deformation of the Roman Rite which some good people erroneously attribute to 'Vatican II'. Pius XII should not be thought of as a Hero of Tradition.
My own personal view is that I would not inconvenience myself in order to attend (2), which is what you will find in the Missal of 1962, mandated by Summorum Pontificum. If you can be happy with Bugnini, you might as well go to a decently performed staging of (3) ... the sort of thing which the Oratories manage so superbly. (Indeed, there are one or two details, such as a fuller provision of Readings at the Easter Vigil, where (3) is more traditional than (2).)
The Priestly Fraternity of S Peter have an indult to use (1) this year. I regard that as a positive move. I hope it is made permanent and universal. In one or two other places which I think I will tactfully not mention, (1) is happily in use. It was the rite employed when the SSPX began its mission in this country.
To be continued.