They do calm down considerably in terms of male/testosterone-driven behavior. Physical changes include a softer coat and a cushier feel to their bodies. Emotional (the hardwired kind) changes include no further interest in a female in heat, no urge to join mating battles, and less win-or-die type of fighting. But the cat is still a cat, and cats like to have the question of who is boss very well understood, and they will always fight or spat over territory. Male or female (I have three male and 2 female alpha wannabe's), they will suddenly begin to assess the strengths, weaknesses, and momentary vulnerabilities of another of the pride and launch themselves into an attack. Sometimes it isn't really serious -- no blood, very little fur flying, short duration of disturbance and later a dignified amnesia. But every so often they wake up in a bad mood --- don't we all? --- and pick desperate, but usually brief, fights where blood is drawn. That's when I use my quiet-time routine, and try to snatch up the aggressor and put him/her in the bathroom, and if the other one has stayed around for a few seconds, the victim and shut him/her in the computer/book room.
#######NOTE!!!!! -- DO NOT touch, pick up, or get within clawing distance of a very angry cat -- or between two angry cats -- unless you are absolutely sure of the bond between you. If their bonding is territorial rather than personal, you can be severely hurt when they are in the fighting mode. If you find yourself in that predicament, do not scream, try to beat or shake the cat off, or shout. Become absolutely still, even if you are bleeding and caught by claws or teeth. Speak soothingly in a soft "mommy to baby" voice. The cat will eventually calm down and pull the claws in and the teeth out. Then you can slowly, very slowly, withdraw the part of your anatomy that is injured. No sudden moves, nothing loud, everything as calm as possible. Clean the wounds carefully under running water, if possible, with plenty of hand soap (a disinfectant hand soup is best, of course). Let the blood flow freely for a while (unless you've got a punctured artery or vein), then just as the first aide books tell you -- pressure on the wounds while you are searching out the adhesive tape and gauze pads and bandaides -- a towel wrapped tightly or pressed against the wound keeps you from bleeding all over the place. Then, depending on the severity of your wounds, either phone someone to take you to the doctor's for stitches, or just go and lie down for an hour or so to get over the shock (elevate the legs with a pillow). The cat will be feeling very stupid and embarrassed at its out-of-control behavior, and may even come around you crying with worry. Do not assume that the cat will repeat this behavior, but be careful for a while until you see that it was just one terrible episode. Do not punish the cat. It doesn't do any good. And he/she won't understand why, anyway. Just be more cautious with that particular cat when he/she is angry.####
As soon as the adrenalin subsides, everything is usually calm again. I have sometimes seen more bitter fighting, but that usually has a long history of swipes and growling sessions and efforts to chase each other away from the food dishes or some favorite sleeping spot. Cats, like people, reach the final straw, and then it is really rather like vendetta. A big problem, then, how to arrange things, especially if both cats are bonded with you personally before their cat-associations and you don't want to lose either of them.
The principal reasons to spay, other than just not supplying millions more kittens to die miserably in shelters or on the streets, are reduction in male genital and urinary illnesses (also avoidance of some cancers, less chance of the cat being injuried in mating fights, and more chance the cat will remain at home and thus avoid becoming stray, which ups the chances of the cat being killed by dogs, poisons, untreated injuries and illnesses, and cars.
I don't know about other people, but I personally don't want any of my cats to be neutralized to the point that they can't fight to save their own lives -- against a dog attack, for example. The same reason I wouldn't declaw any of my cats, in spite of the damage they occasionally do to household things (or to me!). They need to be able to defend themselves and to self-generate the fight-or-flight adrenalin to kick them into survival modes.
In my experience -- going now into the 4th year of taking in strays and ferals -- cats never completely lose their kitten roots. Suddenly my 11-year old lady -- who lost her sense of humor when I adopted the first strays and who now has a very depressive personality -- will find a feather or a milk bottle top or even a piece of wood or a pencil, and she will spend several hours tossing the item up in the air, grabbing it in mid-fall, rolling over and over with it, and playing tag with it as she shoots it across the floor. Cats never seem to lose their provocative little swipes and attacks to shake up their friends, either. No more do people my age give up all playfulness, sillyness, or sense of humor -- or unwarranted verbal attacks on the people around us when we feel grouchy.
Try to walk in the cat's shoes -- er -- paws. Try to observe the whens and whys of aggressive or dominating behavior. A lot of it explains itself if you get yourself more inside your cat's head.