Ubiquitin chains encode signals defining the fates of their modified proteins. Ubiquitin chain-mediated proteasomal degradation is a widespread eukaryotic regulatory mechanism. Yet, heterogeneity of intracellular ubiquitination has precluded systematically comparing degradation capacities of different ubiquitin chains. Here, we monitor cellular degradation and deubiquitination at high temporal resolution after delivery of bespoke ubiquitinated proteins into human cells. Comparing degradation of a model substrate modified with various K48, K63 or K48/K63-branched ubiquitin chains revealed fundamental differences in their intracellular degradation capacities. K48 chains with three or more ubiquitins triggered degradation within minutes. K63-ubiquitinated substrate was rapidly deubiquitinated rather than degraded. Surprisingly, degradation and deubiquitination behaviour of K48/K63-branched chains was determined by the identity of the substrate-anchored chain, establishing that branched chains are not the sum of their parts. Overall, our work reveals a degradation code for ubiquitin chains varying by linkage, length and topology and a functional hierarchy within branched ubiquitin chains.