Dear Suzanne:

Well you do know my take on tattoos.

As mentioned in that post linked above the Chi Rho symbol (or Labarum) is the symbol of Christ. "Chi" and "Rho"are the first two letters in the Greek spelling of the word "Christ." This symbol is the one that the Emperor Constantine saw in a vision with the motto: "On this symbol thou shall conquer." Under this emblem Constantine won his battles. This symbol is also an emblem of my community, the Order of the Legion of St. Michael.

From the 1917 Catholic Encyclopedia:

Labarum is the name by which the military standard adopted  by Constantine the Great after his celebrated vision  (Lactantius, How the Persecutors Died"cross of light", is described by Eusebius (Vita Constant., I:26) as "a long spear, overlaid with gold", which with a transverse bar formed the figure of a cross. "On the top of the whole was fixed a wreath of gold and precious stones, and within this the symbol of the Saviour's name, two letters indicating the name of Christ  by means of the initial letters, the letter X intersection P at the centre." These two letters formed what is known as the monogram of Constantine, so called — not because it was the invention of this emperor, for it had been a familiar Christian symbol prior to his conversion — but because of the great popularity it enjoyed from the date of its appearance on the imperial standards. 44), was known in antiquity. The original labarum, designed under the emperor's direction on the day subsequent to the appearance of the

From the cross-bar of the spear, was suspended a purple banner with the Greek  inscription TOUTO NIKA — i.e. conquer by this (sign), usually rendered in Latin "In hoc signo vinces" (in this sign thou shalt conquer). ...The term labarum, which is of uncertain derivation, was probably familiar in the Roman army from the reign of Hadrian.

As for the Triquetra, it has origins well before Christianity, but among Christians it is used as a sign of the Trinity. It became popular after the Celtic Revival of the 19th century maybe because it is reminiscent of the three-leafed shamrock used by St. Patrick as symbol of the Trinity.

To your question as to which of these symbols has more meaning and strength for the Catholic Church, I would say the Chi Rho. There are many signs of the Trinity that may be used by Protestants and Catholics alike, but the Chi Rho has specific relation to the Catholic Church as the Catholic Church is Christ's Church that leads the battle in this world.

The Chi Rho was the symbol under which Constantine lead his army to defeat the forces of Maxentius at the Battle of the Milvian Bridge in A.D. 312. This symbol, under the banner of "In hoc signo vinces" (in this sign thou shalt conquer), is a symbol of our role and task as soldiers of Chirst. Indeed, under the sign of Christ, through the Catholic Church, the Kingdom of God will reign.

Now, as for a tattoo, if you must do this, whatever you do should be modest. The tattoo should be small. The location of this tattoo, because it is a religious symbol, should not be placed where it cannot be modestly revealed in public, but should still be under normal clothing where it will not readily show. The reason for this deals with getting a job. If you have a tattoo that customers can readily see, even though it is religious in nature, an employer may not hire you.

God Bless,
Bro. Ignatius Mary