Traditionally, the public-sector has been seen a less stress, less money but a better pension. However, this has changed dramatically in recent year. Last I read, the Tories were thinking of getting rid of the National Audit Office — those who effectively audit the public-sector auditors — and if this went ahead it would likely lead to an increasing work-load and responsibility for public-sector auditors, albeit with little extra pay.
Stats wise, the chances are that in the public-sector there will always be work for you to do. So, here it will be more of a case as to whether you are able to complete your audits within the allocated time-frame. In the private-sector it is heavily dependent on who you work for...
If I recall correctly, specific Graduate entry programmes for the public-sector are really competitive. However, standard entry positions tend to be much easier to come by and do not offer that much less.