Do low-cost airlines make more profit than luxury airlines?
It is hard to say for sure - profits will always be relative and in many cases not clear to anyone without advanced economics/accounting qualifications. However, there are a number of differences in terms of customer experience and service that can make a lot of difference to profit. Examples might be:


Crew size - it usually states that the crew on a no frills airline
are there for customer safety rather than service - on a legacy
carrier they are (technically) there for both so there are more of
them
What's included - rather than charging separately for things like
seat selection, baggage and meals, a 'frilly' (as opposed to 'no
frills) carrier will bundle them together, earning less than an
airline that charges them separately. Note - BA and a few other
airlines do charge separately for seat selection
Operating efficiency - a no frills aircraft typically spends less
time on the ground being turned around, so this expensive asset is
utilised with a higher percentage air time
Seat pitch - a smaller seat pitch means two or three additional rows
of seats in an aircraft - so greater profits per flight
Less straightforward pricing models - in many cases, a 'low cost'
airline charges more for a ticket than a standard airline, hiding
behind clever yielding of fare and additional costs added on later in
the booking process. In the travel industry I have seen time and
again people being fooled by the term 'low-cost airline'


I am sure there are many more. The operational efficiency of individual aircraft can be quickly worn away when a 'frilly' airline is required to compete with a 'no frills' on a similar route. Also, some 'flag carrying' airlines, which tend to make much greater use of joint ventures and codeshare agreements than no frills airlines, sometimes fly routes because it is a requirement of a larger deal - and if that is not very profitable (or even loss-making) it can drag down overall profit.