When I am using the CVs, I mostly run Fighter heavy, with bombers when the ramps are available.
That means my enemy targets are bombers and scouts, with scouting duties until fuel runs out.
At some point during some games I completely give up trying to clear the skies of local scouts and fighters over my side's BBs because I lose too many fighters to knuckleheads in AA ships that shoot at everything. (They're the same guys with HH that spray it all over, sinking friendly subs and hitting ships without any remorse whatsoever). That's when I load my bombers up and just use the fighters for scouting duties and bomber path protection.
My fighters are all T4+ and can easily intercept all bomber classes, so I focus on that. I don't hear too many notes of appreciation for taking down 11 enemy bombers headed towards my BB line either.
However, an unattended fighter will circle-of-stupidity with a scout anywhere, anytime it isn't being closely watched. With 8 squadrons of planes in action, one or two planes that get distracted just happen occasionally.
Conversely, I've seen many games were one or two competent AA ships can keep an enemy blind and protected as good or better than any fighter support. A hard blast of AA on a tight formation can drop 3 or 4 planes instantly.