All 3-register Type XX pieces feature a flyback movement, but which one depends on the manufacturer and time period. The flyback mechanism was invented by Breitling in 1932 and patented by Longines-Francillon in 1936 ( with patent number 183262).
I have found clear movement stamping on the plate for only four pieces, two each of Valjoux 225 and 720.
If you search text descriptions of these pieces, including those posted by the owners or auction houses, you will find incorrect references in the text descriptions. Movements attributed to the Mathey-Tissot Type XX include the following Valjoux movements: 22 (no), 222 (nope), 225, 720 and Valjoux 72 (no again). For those flyback lovers, Ranfft also lists 230, 235, 237, and 725 as being flybacks.
I have never seen the movement firsthand of a 3-register GP Type XX, and the images that I have are not clear enough to see what the stamping indicates (I believe they are the Valjoux 720 based on images, but I can’t say definitively).
All references in posts on the Girard-Perregaux Type XX indicate that the Valjoux 720 was used. This seems reasonable, though I would not be surprised to see examples using the Valjoux 225.
Approximately half of the movements seen show with import code of GXM, indicating they were for the U.S. market.
As with the Girard-Perregaux, I have never seen a movement firsthand of a 3-register Breguet Type 20, and in the few images available we see the Valjoux 225 only. Many posts reference the Valjoux 720, which was also likely used.
The Breguet Type 20 has either the Valjoux 225 or Valjoux 720 movement, with either a 15 or 30 minute counter. It seems likely that the Mathey-Tissot and Breguets began production first, with the Girard-Perregaux following in initial production date.
As an aside, I have read some sites claim that the Valjoux 720 was limited to 200 pieces, though given serial number information and the quantity found, this seems unlikely.
My understanding of related Valjoux movements :
– Valjoux 22x: Valjoux 22 does not have a flyback, nor hour register. The Valjoux 222 is a modified 22 with the addition of a flyback function, used in 2-register Type XX timepieces. The Valjoux 225 is a Valjoux 222 with the addition of an hour subregister.
– Valjoux 23x: Valjoux 23 does not have a flyback, nor hour register. Valjoux 231 and 235 both are flyback, again used in 2-register Type XXs. Valjoux 230: 2 register, flyback 
– Valjoux 72x: The Valjoux 72 has three registers and no flyback function, whereas the 720 adds the flyback function. The 725 has flyback, introduced in the 1970s, with a higher beat rate . The 725 “minute register is usually 30 minutes, but can be 15 minutes in the 2nd generation Breguet Type 20…”, which interestingly is similar to what we see for the Mathey-Tissot 3-register Type XX.
 The original Type 20 military chronographs, Don Indiano
 The famous Valjoux column wheel family of chronographs, John Hannover