You left out the "Iron" fly, which is a straddle/strangle, using both puts and calls so, by definition, the outer strikes will always be less than the middle strikes. (OTM calls above and puts below).
That was sort of the go to, standard fly that was used during my years on the floor.
Also, whether buying or selling a fly was the most profitable choice at any given time had less to do with "theory" and everything to do with "pricing".
Neither buying, nor selling, a fly is a "better" strategy than the other.
It is all about the pricing of that fly .
In all of my years on the floor, the single most profitable trade, for everyone, at that point in time, was selling ATM fly's for 30% of the distance between strikes.
This was in crude oil mostly,( but pretty much in everything at that time), which at that time was moving through 2-3 strikes, several times a day, everyday.
We would buy the ATM straddle, and sell the next higher call, and lower put, and pay 30% debit of the distance between strikes.
For example, with crude at $70, we would buy the $70 straddle, and sell the $69 put, and $71 call, for a debit of .30 for a $1.00 wide fly.
Unlike stock options, which are x100 (shares), crude options are x1000 (barrels), so .30 = $300 (not $30).
As the price moved away from ATM ($70), the fly would immediately gain in value, and when it reached the next strike, would be priced at .60-.70 ( 100%+ gain).
Crude would travel past 2-3 strikes, back and forth several times a day.
So, buying the middle, and selling the wings "can" be the most profitable strategy there is IF the "pricing" favors it.
Our rule of thumb, which I would still use today, is to be able to sell a fly for 30% of the distance between strikes.
Given my history with this, I am always looking for this opportunity, which pretty much never exists in stocks, but does in various commodities from time to time.
This was a trade, like any other trade in history, that was discovered by a few people, and worked 100% of the time.
Then, as more and more people became aware of it, and more people used it, the pricing obviously would change, ultimately pricing itself out of having an edge.
But, because there was no retail access to this at that time, or personal computer trading platforms, this opportunity lasted 2-3 years before becoming too crowded and pricing itself out of profitability.
So no strategy is "better" than another ...what makes one the best opportunity is the "pricing" of that strategy.
And if a particular position becomes too popular, and therefore too "crowded", by definition the reverse has to be the best approach, because of the imbalance of liquidity.
Prices follow the "path of least resistance", and if most participants have a position on the same way, they will eventually need someone to be there to take the other side when they try to exit the trade.
This is why , more often than not, movement occurs that does not make "logical" sense.
There is tremendous opportunity in being "contrarian" when used properly, for these reasons.
These trade cycles are as old as the markets themselves... there is nothing new here, just the way it plays itself out in different situations, during different times.