On paper the matchup is 6-4 akuma because of Akuma's zoning potential with his fireballs but that will all go pear shaped if you get predictable, allow yourself to get pushed into the corner, or if you suffer from my main problem in this matchup and get bored of dinking away at 1100 health.
After a sweep, use light demon flip palm OS sweep to beat lariat, do the demonflip slightly later and you can go for a throw. Divekicks will pretty much lose to the 'magic lariat'. (holding down to lower their hurtbox until the last moment and then pressing 3p)
Neutral jumping against gief at point blank range is a nono, at best you will eat a clean magic lariat, at worse you will trade and he will EX greenhand you. Backdash is a slightly safer option but still has its risks, unfortunately this advice is useless but you can't drop combos in this match because it's not only lost damage and followup mixups, it's lost health.. it's twice as bad.
Try and bait ex greenhand by jumping and wiffing a normal, keep the gief on edge about when you're actually gonna throw a fireball
This is my problem also, I was doing well when I started to zone but I get bored and want to 'get in'. Thanks for the tips I'll keep these in mind, thank you also Hyv for your suggestions. It's really my own fault, as you said you can't drop combos especially with somebody who does damage like Gief.