I probably do not surprise anyone if I claim that how much to tax capital income and bequests is controversial. In the United States, it is due a divergent beliefs about the motivation of entrepreneurs and luck of being born in the right environment. In Europe, arguments center on fairness. The literature does not help much, with results being very sensitive to income processes, market features and preferences. Capital income is generally taxed less than labor income, often not at all, and results on bequests vary wildly, again often with zero tax results.
Thomas Piketty and Emmanuel Saez add to this bewildering literature with a tour-de-force, a very rich, yet tractable model that allows to disentangle quite a few effects and illustrate what influences these taxes, in particular parameters that can be estimated. The richness is necessary to relate the model to real world better than the extant literature which yields this unrealistic and unobserved zero tax result. It is impossible for me to summarize over 100 pages in a few paragraphs, so here is a short overview.
The model features a large degree of heterogeneity, in taste for bequests and wealth accumulation, and in labor ability. Hence labor income and inheritance are not highly correlated, allowing for a trade-off between capital and labor income taxes because, as Piketty and Saez put it, two-dimensional inequality requires two tax tools. The tax on bequests is higher if bequests represent a large fraction of output, if the aggregate elasticity of bequests with respect to their tax is high, and if the taste for bequests is low. Tax rates on bequests can go all the way to 80%, and are for most parametrizations much higher than for labor income. This is because in general labor income should be favored, as it is derived from ability, unless people really like leaving bequests a lot.
If markets are imperfect and there is risk in capital return, then tax rates of capital income and bequests start differing. The lifetime equivalent of the capital income tax is then much higher than the bequest tax rate. because return fluctuations have stronger impact on periodic capital income than bequests, which are mostly accumulated capital and labor income. Important in this is also that in all economies, most people receive very little if any at all in terms of inheritance. This makes results remarkably robust with respect to welfare criteria.