You should go for case 2 - document reference.
If you start to get a lot of traffic, you will end up having photo documents with hundreds or even thousands of comments and likes inside.
You would have a data structure like:
collection: photos
{
    "_id": ObjectId("5c53653451154c6da4623a79"),
    "name": "ocean",
    "path": "path/to/ocean.png"
}
collection: photo_comments
{
    "_id": ObjectId("c73h42h3ch238c7238cyn34y"),
    "comment": "it's actually a lake",
    "photo": ObjectId("5c53653451154c6da4623a79"),
    "user": ObjectId("sd686sd8ywh3rkjiusyyrk32")
}
collection: photo_likes
{
    "_id": ObjectId("x267cb623yru2ru6c4r273bn"),
    "photo": ObjectId("5c53653451154c6da4623a79"),
    "user": ObjectId("sd686sd8ywh3rkjiusyyrk32")
}
You can get more details at Model One-to-Many Relationships with Document References.