If you wish to progress while staying in the public sector, your experience in the ministry will definitely be beneficial as opposed to starting out in the stat board, as you're exposed to big picture right from the start. In addition, if you are to be chosen for those management programme, you will still need to be seconded to the parent ministry if you're from a stat board, to be assess by the PS. That's at least 1 - 2 years lost in proving yourself again.

In addition, whatever increments announced for civil servants, you can be sure that you'll get it. If you're in stat board, depending on which stat board you're in, you may not get it. So in the long run, your base salary will lose out to those in ministries (unless you're in tier 1 stat boards).

Finally, my personal experience is that it's always easier to jump from ministry to a stat board, and not the other way round. Reason being stat board always welcome those from ministries (especially parent ministries) because they know how the sector works, and have the big picture experience.