What do Catholics think of the Philokalia? The absence of a "mysticism"-oriented text in Catholic Christianity has always struck me. The Philokalia are an incredible source of ascetic instructions for the believer who seeks communion with God. 

(1) In what consideration do Catholic Christians keep the Philokalia?
And, (2) is there a similar text in the Catholic tradition?
The Catholic Church has no problem with the Philokalia; it is a legitimate mystical text in the Eastern Christian tradition. Eastern Catholics make use of it all the time. (I am not aware of any official pronouncement by the Magisterium, but all of the authors are well regarded monks.)

As far as mysticism in the Western Church, there is not a “single” work, but there is long tradition of mysticism. For example, among many others works, there is the following:


El castillo interior (The Interior Castle) of St. Theresa of Avila.
The works of St. John of the Cross.
The works of St. Hildegard of Bingen.
The works of St. Bernard of Clairvaux.
Many works inspired by the writings of (Pseudo)-Dionysius the Areopagite, including the anonymous Cloud of Unknowing.