The second is almost correct:

{
    "foos" : [{
        "prop1":"value1",
        "prop2":"value2"
    }, {
        "prop1":"value3", 
        "prop2":"value4"
    }]
}

Lean towards option 1, as it's a more expected format.

Option 1 works with JSON as it's designed to be used and therefore benefits from what JSON offers (a degree of human readability, which is good for debugging, and straightforward parsing, which is good for limiting entire categories of bugs to begin with).

Option 2 begrudgingly adopts JSON and subverts many of the benefits. If you don't want human readability, use protobuf or something similar... AIWalker's "CSV"-like approach isn't terrible either. It is marginally better (readable) than splitting objects apart and recombining them. But, this is still not as good (readable) as using JSON "as designed".

Also bear in mind, your API responses are also likely going to be gzipped. Most of the repetition in option 1 will be quickly and transparently condensed over the wire.

As an aside, if you're moving a lot of data, also consider JSONL or paginated results. Pagination can be especially helpful for web clients, as it places natural pauses in the processing, providing a degree of "organic" protection against UI lockups.