We compare wealth taxes and capital gains taxes in a random growth model with idiosyncratic investment risk. At equal tax revenue, wealth taxes generate higher wealth inequality but also higher wealth mobility than capital gains taxes. The mechanism operates through variance: wealth taxes shift the mean of post-tax wealth growth without affecting variance, while capital gains taxes compress the upper tail and reduce variance. Lower variance compresses the stationary distribution, reducing wealth inequality, but also dampens rank changes, reducing wealth mobility. The variance effect dominates the fact that lower inequality shrinks the wealth gaps agents must overcome. Policymakers who value both low wealth inequality and high wealth mobility therefore face a trade-off. This trade-off is robust to type and scale dependence in returns, hand-to-mouth households, aggregate risk, and tax progressivity.