It's a bit of an apples to oranges comparison to say AA accomplished more than Atkins in 5 years vs 8 years because Atkins had to rebuild the organization from the ground up after Anthopoulos emptied the farm system on the way out of the door. AA would have been left with the same challenges rebuilding the team and would have been unlikely to make any more post season appearances during his next 3 years as GM had he chosen to stay. Assuming a similar 3 year rebuilding window now you are left with a GM who made the playoffs twice in an 9 year span, which certainly changes the calculus of the overall discussion to a great degree.
I think Atkins was in the learning phase in his first few years as Blue Jays GM, and much like Anthopoulos he has made some mistakes along the way which can serve as learning experiences. He really should have gotten more in return for Josh Donaldson than Julian Merryweather, and even qualifying Donaldson and letting him walk in free agency likely would have been preferable to get a compensation pick in return. The Grichuk extension was a mistake as there was no rush to extend the guy as he hadn't even reached arbitration yet. This was a pretty small dollar deal so didn't hamstring the organization to a great degree, but I think this was a learning opportunity to avoid early career extensions before gathering enough data beforehand. This likely helped Aktins avoid making a giant mistake by offering Vlad a franchise player extension after his monster 2021 season. I think some of the early career duds for Atkins were during a bit of a murky period where the team was looking to remain at least semi competitive vs a complete tanking style rebuild, as there were no big deals handed out in free agency and none of the better prospects were traded to supplement the major league team either as the organization chose to build from within. Signings like Pierce, Garcia, Roark, Morales etc. were all ultimately regrettable for the most part but all of these were low value bargain hunting/reclamation style signings which were likely hoping to gather tradeable assets that could be moved at the trade deadline.
Ultimately Atkins tenure as Blue Jays general manager is going to be defined by his ability or lack thereof to get the team over the hump to allow them to have success in the post season. He's built a solid window of contention with a homegrown core supplemented with free agent signings and trades. The team has certainly grown expensive and it will be difficult to sustain contention moving forward due to the financial challenges posed by the core growing increasingly expensive. The front office needs to start replacing the aging veterans with younger cost controlled players sooner rather than later if the window of contention is to be sustained past Vlad and Bo's remaining years of control.