Buy a server or cloud computing for a new lab?
Local servers are likely to be substantially cheaper and also faster to access the data over LAN rather than the internet for data on that scale (just for a quick count from AWS you're looking at $2400 per month if you ignore the deep-storage options that are not appropriate for data in-use; for the same price you could pay for local servers in a couple months with the same capacity).

Given similar choices, the labs I've worked in have always opted for local storage, but we also utilize cloud options for sharing data both for personal use (i.e., having access at work and home) and between other labs. However, this is only a subset of the data, for example data extracted or summarized from raw data.