Due to the combat mechanics for air units, most battles will see the attacker or defending fighter killed. If you are attacking a city defended by 8 fighters you will need an overwhelming numbers advantage. I think losing as many fighters as you did was on the unlucky side. Usually fighters will not be shot down by intercepting land/sea units unless the fighter is damaged.
I'm not 100% sure about this but combat promos on fighters seem to make a big difference to the odds of surviving dogfights. Also, never try to use regular fighters against an opponent with jet fighters. It will end in tears.
Fighters vs Jets depends upon the number of promos. CIV fighters (Cha with some crap or a long air war prior) can do reasonably well against jets. Just send in a few suicide units and the high promo fighters will down the jets.