Speed
Aerospike is faster. Almost any system will be quick with low load or simple data access but Aerospike has stayed consistently fast by optimizing for in-memory and SSD-based storage options. Mongo is fast when used with lots of RAM where for caching but is otherwise slow and has low write performance.
Reliability
Aerospike is very stable, although with simpler data access. MongoDB has historically been problematic with persisting data and failover but is much better now. Because Aerospike has better performance and easier management, it leads to less potential problems when scaling.
Setup/Configuration
The clustering with Aerospike is much easier to setup since all nodes are the same and the client drivers handle connections and failover automatically. MongoDB can be easier if you're setting up a single server as it runs on more platforms natively and you can start it without any configuration.
MongoDB has two major ways of clustering, replica sets (for availability) and sharding (for scalability). We had 5 shards and each shard had a replica-set of 3 servers. That's 15 servers to hold data. Then we had 3 config servers that maintained the cluster configuration and had to add 2 arbiter processes after our first major outage to deal with properly escalating a slave to master. That's a lot of moving pieces and also makes it incredibly hard to change your layout in the future.
In contrast, Aerospike has took much less effort but requires more configuration, most of which cannot be changed once the cluster has started whereas with MongoDB you can create and alter databases anytime.
Aerospike does have the ability to sync multiple clusters (which is complicated to setup) so you can have different active datacenters replicating data and accepting writes, something that MongoDB doesn't really support at all.
Data Access
MongoDB has database/collection/document where each document is just json. Aerospike has namespace/set/record where each record is a collection of key-value "bins", which can then have nested key/value structures. Namespaces are pre-configured and are not dynamic, and names for properties are limited to 14 characters which is annoying to work with.
Both have secondary indexes although MongoDB lets you query immediately by anything while Aerospike requires index setup or custom scripting. Both have built-in aggregation frameworks. Aerospike clients support LUA scripting but MongoDB supports map-reduce and custom javascript functions.
It really depends on what your application needs, but MongoDB wins in flexibility, easier querying and less restrictions.
Cost
Both are now open-source and free. Both have enterprise versions with extra features, but licensing is expensive if you have lots of data. Aerospike might be cheaper since it requires less machines for the same performance.
Overall
For most scenarios, I would recommend Aerospike. The document-store semantics and flexibility of MongoDB are great but scaling and maintaining it as a distributed database is painful. Aerospike is fast and reliable and can run with fewer nodes that are easier to scale.
January 2016: MongoDB has released MongoDB Cloud Manager which is a paid SaaS service that can provision and manage your clusters. This solves a lot of the trouble with configuring Mongo.
March 2017: Both databases have come a long way. Aerospike now has faster replication and more flexible config settings without restarting the whole cluster. MongoDB has new schema enforcement, better performance and even supports joins along with MongoDB Atlas managed service to take away all the scaling issues.
I now highly recommend ScyllaDB which is a Cassandra compatible open-source database with incredible performance, multi-datacenter replication, and no limits on usage.
