An accepted solution is a solution to the original poster’s question.
A best answer is someone’s subjective opinion of the best response from a range of answers.
The distinction is important. The former is based on facts, the latter is based upon opinions.
The original poster is best qualified to mark an answer as an accepted solution. She knows better than anyone whether it solved her problem or not. No promise is being made other than it solved the problem for 1 person. If it helps others too, great.
The original poster is less qualified to select the best answer from several responses. That requires expertise in the topic (expertise they might not have if they’re asking the question). The premise is different. ‘This might not solve your problem, but it’s the best answer we’ve got here.’
Both can be abused and misused.
Two useful principles here:
1) Accepted solutions are ideal for support communities. But they need automated prompts to the poster to mark an answer as an accepted solution or allow other members to highlight if an answer worked for them (with a limit i.e. 3 tags) for that answer to be marked as an accepted solution. Customer support staff can skim other responses and mark successful answers.
2) Best answers are ideal for customer success communities with a focus on helping others learn from each other. Here it helps to allow top members in the insider/mvp/superuser program mark an answer as best.
Don’t fall into the trap of confusing what’s based upon facts and what’s based upon opinions.