As Jaydill said....with A.I. you have the chance to bring in better bulls into your herd. You can pick bulls that have already proved themselves. You can more compliment each cow individually. If you have a cow that is leathery in the front, you can choose a bull for that cow that is known to clean up the front end. If you have a cow that needs some more meat in the rear you can choose a bull that compliments her.
The downside to A.I. is there is lots more time involved, you have to watch for heat cycle, you have to haul them or have someone come to your place to breed them, unless you learn yourself. You call have less accuracy on A.I. maybe only around 60% bred, some times better some times worse. Then you have to start all over watching that cow and doing it again.
Plus for a bull, is you have less time involved watching you cattle and you will get a higher conception rate.
Downside to a bull is more of a pain in containing him, you have the cost of feeding him and vet bill etc....You will have to eventually sell and get a different bull if you are keeping your own replacements. The bull might work to better some of your cows but maybe he is not what is needed on all them. Limited genetics.