The existing literature on inequality between private and public sectors focuses on cross-section differences in earnings levels. A more general way of looking at inequality between sectors is to recognize that forward-looking agents will care about income and job mobility too. We show that these are substantially different between the two sectors. Using data from the BHPS, we estimate a model of income and employment dynamics over seven years. We allow for unobserved heterogeneity in the propensity to be unemployed or employed in either job sector and in terms of the income process. We then combine the results into lifetime values of jobs in either sector and carry out a cross-section comparative analysis of these values. We have four main findings. First focusing on cross-sector differences in terms of the income process only, we detect a positive average public premium both in income flows and in the present discounted sum of future income flows. Second, we argue that income inequality is lower but more persistent in the public sector, as most of the observed relative cross-sectional income compression in the public sector is due to a lower variance of the transitory component of income. Third, when taking job mobility into account, the lifetime public premium is essentially zero for workers that we categorize as "high-employability" individuals, suggesting that the UK labor market is sufficiently mobile to ensure a rapid allocation of workers into their "natural" sector. Fourth, we find some evidence of job queuing for public sector jobs among "low-employability" workers.