It is usually better to do this kind of analysis towards testing some hypothesis or answering a biological question. This being said, for exploratory purposes, you could do the typical enrichment analysis for pathways, GO terms and whatever you think could be useful e.g. protein domains. For phosphosites, you could start by counting the number of phosphorylated proteins then the total number of sites you've identified followed by checking how many already known sites you've found (using e.g. Phospho.ELM or PhosphoSitePlus as sources of known sites). You could also do the enrichment analysis on the phsophoproteins. Then you could also go for identification/prediction of putative causal kinases (e.g with PHOXTRACK) then try to figure out if some kinases are activated in one condition vs the other.