I work in education.
Impossible to generalise, there are good and bad academies just as there are maintained schools.
Pros and cons can often relate to what the LA is like and the services it provides. Maintained schools have their budgets topsliced to fund LAs, so if the LA is hopeless as a headteacher you may well question why you're paying that and think you're better off having that money direct.
But if you join an academy chain they'd take chunk too.
The whole matter is incredibly complicated though and there are many variations across the country.
That's why your accountability question is hard to answer. In the simplest form academies are accountable directly to the DfE chopping out the LA middleman. But these days most academies are in a chain or multi academy trust (MAT) so the middle man becomes the MAT.
My children are older now but if I were starting out again I'd visit the school, think about its reputation in the community, read the ofsted and go with my instincts and not worry too much about whether it's an academy.
One canny question to academies could be whether teachers are paid according to Schoolteachers' Pay and Conditions Document (STPCD). This is automatic for maintained schools and optional for academies but many choose to stick with it. Those that don't will often have some unwelcome small print in contracts which can translate into poor morale and high staff turnover.
If you get any reticence to answer this look on the website at job vacancies.
Another warning sign is that some academies especially in the primary phase have very little autonomy and are controlled with a rod of iron by the trust board/MAT/secondary school at the top of the chain.