There are very few tourbillon chronographs out there. So, there isn't much information on the platinum Breguet 3577. (2.5hz in 2005) “Grande Complication”.
There is a little information about the movement. The 554.2 (manual winding) is built on the 533.3 chronograph. You can see the similarity in the layout between the 554.2 and 533.3.
In turn, the 533.3 is based on the respected Lemania CH 27 (dates to the 1940s). As late as 2013, the 533.3 had been used in the Classique Chronographe 5287 3hz.
https://www.hodinkee.com/articles/hands-on-with-the-breguet-classique-chronograph-5287-live-pics-pricing
The 554.3 (silicon balance spring) superseded the 2.5hz 554.2 used in the 2005 Breguet 3577, when the Marine tourbillon chronograph 5837 (diameter 42mm) was launched in (?).
Interestingly, there are no plates protecting the movements. Indication that these are movements of the old school, where transparent backs were unheard of.
Fittingly, Breguet has a long and distinguished reputation for superior complications. They offer many tourbillon models. Some fitted with a PC or chronograph complication. Even a repeater with PC (Ref 5447).
Oddly, Breguet only offers a tourbillon chronograph today in the Marine (Ref 5837) series, no longer as a Classique (?)
Bottom line: The Breguet tourbillon chronograph 5377 is attractively priced today as pre-owned prices seem to have plunged in the last 5 years. However, it is a complex movement and your ownership of an old watch is likely to be an 'interesting' relationship. I'm not sure that I have the stomach for it.
Anyone like to add their thoughts?