MongoDB structure: single collection vs multiple smaller collections
I would recommend NOT to make separate collection per user.
Read the documentation
By default MongoDB has a limit of approximately 24,000 namespaces per database. Each namespace is 628 bytes, the .ns file is 16MB by default.
Each collection counts as a namespace, as does each index. Thus if every collection had one index, we can create up to 12,000 collections. The --nssize parameter allows you to increase this limit (see below).
Be aware that there is a certain minimum overhead per collection -- a few KB. Further, any index will require at least 8KB of data space as the b-tree page size is 8KB. Certain operations can get slow if there are a lot of collections and the meta data gets paged out.
So you won't be able to gracefully handle it if your users exceed the namespace limit. Also it won't be high on performance with the growth of your userbase.
UPDATE
As @Henry Liu mentioned in the comments. For Mongodb 3.0 or above using WiredTiger storage engine, it will no longer be the limit.
MongoDB is great at scaling horizontally. It can shard a collection across a dynamic cluster to produce a fast, querable collection of your data.
So having a smaller collection size is not really a pro and I am not sure where this theory comes that it is, it isn't in SQL and it isn't in MongoDB. The performance of sharding, if done well, should be relative to the performance of querying a single small collection of data (with a small overhead). If it isn't then you have setup your sharding wrong.
MongoDB is not great at scaling vertically, as @Sushant quoted, the ns size of MongoDB would be a serious limitation here. One thing that quote does not mention is that index size and count also effect the ns size hence why it describes that:
Thus if every collection had one index, we can create up to 12,000 collections. The --nssize parameter allows you to increase this limit (see below).