I am open to the possibility that this is just a function of my hard heart, but for me accountability inevitably has a whiff of legalism about it. The idea is that there is a standard, and I am going to be questioned on whether I have attained it or not. I am being held accountable for whether I have or have not done something. That is not unreasonable, but I'm afraid that the sort of behaviour it promotes in me (and I cannot speak for anyone else) is outward conformity and avoidance. Inwardly, what it promotes is guilt, because I know that really I am far more sinful than any 'accountability partners' will ever know.
Confession, on the other hand, begins with the premise that I have failed. It doesn't flex the high standard that accountability seeks to enforce, but it does assume that I have not kept that standard. And then it invites me to relate my particular sins to another human being. An insight from Derek Tidball:
The personal verbal confession of sin assists a person to accept his moral guilt and view it in the same light as God does. It is to easy to fool oneself and only pretend confession is accomplished simply by mulling it over in the mind.I think that's right! My supposed confession of sin to God easily becomes actually a monologue - me, by myself, pondering my failings. In that monologue, I do not feel the force of guilt (because I am not forced to bring my sin into the light of another person's presence), nor do I ever really deal with sin (because it is just an object of thought, not a concrete thing). Confession to another human being aids confession to God.
But the big thing that is present in the idea of confession but absent, or at least marginalised, in that of accountability is absolution. When I confess specific sin to another Christian, it is there job to present the gospel! As I confess to them, they stand proxy for God - they are his ministers and priests - receiving my confession and pronouncing, in God's name and through the gospel, forgiveness of sin. And so the matter is dealt with.
What this means (in very black and white and somewhat caricatured terms) is that accountability tends toward a programmatic approach to holiness - it is about how can I do and be better - whereas confession is about a relational approach - it is about how my sinful self can genuinely enjoy the experience of forgiveness and deep fellowship with God.
Of course, there is significant overlap between accountability and confession, and I wouldn't suggest ditching the former! I will still keep my accountability software running. But perhaps a different approach - perhaps the recognition that even my accountability is a sort of general confession of sin and inability, rather than just a sensible precaution - perhaps that might help to keep the gospel central and our relationship with God at the fore.