OK, facts only:
1. Scheduled services: the only route that both operators have in common is ANTIGUA (ANU) - ST BARTHS (SBH)
SBC: €300 EUR ($340 at today's exchange rate)
TWA: $495 USD
Booking simulations made for a one way flight ANU SBH on March 11th on operators websites.
2. Private Charter Services (one way rates)
SAN JUAN (SJU) - ST BARTHS (SBH)
SBC: €3,900 EUR ($4,400 USD)
TWA: $3,950 USD non holiday - $4,950 USD holiday
ST THOMAS (STT) - ST BARTHS (SBH)
SBC: €2,900 EUR ($3,280 USD)
TWA: $3,950 USD non holiday - $4,950 USD holiday
ANTIGUA (ANU) - ST BARTHS (SBH)
SBC: €1,400 EUR Low Season - €1,500 EUR High season ($1,590 USD - $1,700 USD)
TWA: $3,960 USD (8 seats on the Scheduled service, so as to "Privatize the flight").
SBC is all taxes & fees included, TWA is not.
It appears that TWA is substantially more expensive than SBC on most routes.