For all time of the game to me the straight flush came out only 3 times. All these 3 times were nuts. In order to win one straight flush from another straight flush - the probability of such a situation is about 1/10 000 000. Such an event is very unlikely.
An example of such unlikely events - What is the probability that 2 opponents have gone all-in with pocket AA and one had the flush on the board?
Although rare, the odds of AA beating AA are not in the same ballpark as straight flush over straight flush. AA v AA occasionally happens and both players will almost always be all-in pre-flop, ensuring the necessary runout. By contrast, one reason straight flush over straight flush is so rare is because the low end cards are not always played, and the river is often not reached. But, all it takes after AA and AA are dealt is for any four suits to fall on the board. It happened in a famous hand between Connor Drinan and Cary Katz during the 2014 $1,000,000 WSOP Big One for One Drop. Enjoy the watch.
According to my research/math: The odds of two players getting the same pocket pair are 1 in 294. Since there are 13 ranks, the odds of two players specifically getting ACES in the same hand are 294 x 13 = 1 : 3,822. Four cards to a flush or a flush on the board happens around 5% of the time, and will almost always win for the player holding the correct Ace. So, Aces will crack Aces roughly once every 76,440
hands (20 x 3,822). Making it very rare, but at least an order of magnitude less rare than straight flush over straight flush.