Extant protein-coding sequences span a huge range of ages, from those that emerged only recently in particular lineages, to those present in the last universal common ancestor. Because evolution has had less time to act on young sequences, there might be "phylostratigraphy" trends in any properties that evolve slowly with age. Indeed, a long-term reduction in hydrophobicity and in hydrophobic clustering has been found in previous, taxonomically restricted studies. Here we perform integrated phylostratigraphy across 435 fully sequenced and dated eukaryotic species, using sensitive HMM methods to detect homology of protein domains (which may vary in age within the same gene), and applying a variety of quality filters. We find that the reduction in hydrophobic clustering is universal across diverse lineages, showing limited sign of saturation. But the tendency for young domains to have higher protein structural disorder, driven primarily by more hydrophilic amino acids, is found only among young animal domains, and not young plant domains, nor ancient domains predating the existence of the last eukaryotic common ancestor. Among ancient domains, trends in amino acid composition reflect the order of recruitment into the genetic code, suggesting that events during the earliest stages of life on earth continue to have an impact on the composition of ancient sequences.