Application Level sharding: dbShards is the only product that I know of that does "application aware sharding". There are a few good articles on the website. Just by definition, application aware sharding is going to be more efficient. If an application knows exactly where to go with a transaction without having to look it up or get redirected by a proxy, that in its self will be faster. And speed is often one of the primary concerns, if not the only concern, when someone is looking into sharding.
Some people "shard" with a proxy, but in my eyes that defeats the purpose of sharding. You are just using another server to tell your transactions where to find the data or where to store it. With application aware sharding, your application knows where to go on its own. Much more efficient.
The best approach for sharding MySQL tables to not do it unless it is totally unavoidable to do it.
When you are writing an application, you usually want to do so in a way that maximizes velocity, developer speed. You optimize for latency (time until the answer is ready) or throughput (number of answers per time unit) only when necessary.
You partition and then assign partitions to different hosts (= shard) only when the sum of all these partitions does no longer fit onto a single database server instance - the reason for that being either writes or reads.
The write case is either a) the frequency of writes is overloading this servers disks permanently or b) there are too many writes going on so that replication permanently lags in this replication hierarchy.
The read case for sharding is when the size of the data is so large that the working set of it no longer fits into memory and data reads start hitting the disk instead of being served from memory most of the time.
Only when you have to shard you do it.
The moment you shard, you are paying for that in multiple ways:
Much of your SQL is no longer declarative.
Normally, in SQL you are telling the database what data you want and leave it to the optimizer to turn that specification into a data access program. That is a good thing, because it is flexible, and because writing these data access programs is boring work that harms velocity.
With a sharded environment you are probably joining a table on node A against data on node B, or you have a table larger than a node, on nodes A and B and are joining data from it against data that is on node B and C. You are starting to write application side hash-based join resolutions manually in order to resolve that (or you are reinventing MySQL cluster), meaning you end up with a lot of SQL that no longer declarative, but is expressing SQL functionality in a procedural way (e.g. you are using SELECT statements in loops).
You are incurring a lot of network latency.
Normally, an SQL query can be resolved locally and the optimizer knows about the costs associated with local disk accesses and resolves the query in a way that minimizes the costs for that.
In a sharded environment, queries are resolved by either running key-value accesses across a network to multiple nodes (hopefully with batched key accesses and not individual key lookups per round trip) or by pushing parts of the WHERE clause onward to the nodes where they can be applied (that is called 'condition pushdown'), or both.
But even in the best of cases this involves many more network round trips that a local situation, and it is more complicated. Especially since the MySQL optimizer knows nothing about network latency at all (Ok, MySQL cluster is slowly getting better at that, but for vanilla MySQL outside of cluster that is still true).
You are losing a lot of expressive power of SQL.
Ok, that is probably less important, but foreign key constraints and other SQL mechanisms for data integrity are incapable of spanning multiple shards.
MySQL has no API which allows asynchronous queries that is in working order.
When data of the same type resides on multiple nodes (e.g. user data on nodes A, B and C), horizontal queries often need to be resolved against all of these nodes ("Find all user accounts that have not been logged in for 90 days or more"). Data access time grows linearly with the number of nodes, unless multiple nodes can be asked in parallel and the results aggregated as they come in ("Map-Reduce").
The precondition for that is an asynchronous communication API, which does not exist for MySQL in a good working shape. The alternative is a lot of forking and connections in the child processes, which is visiting the world of suck on a season pass.
Once you start sharding, data structure and network topology become visible as performance points to your application. In order to perform reasonably well, your application needs to be aware of these things, and that means that really only application level sharding makes sense.
The question is more if you want to auto-shard (determining which row goes into which node by hashing primary keys for example) or if you want to split functionally in a manual way ("The tables related to the xyz user story go to this master, while abc and def related tables go to that master").
Functional sharding has the advantage that, if done right, it is invisible to most developers most of the time, because all tables related to their user story will be available locally. That allows them to still benefit from declarative SQL as long as possible, and will also incur less network latency because the number of cross-network transfers is kept minimal.
Functional sharding has the disadvantage that it does not allow for any single table to be larger than one instance, and it requires manual attention of a designer.
Functional sharding has the advantage that it is relatively easily done to an existing codebase with a number of changes that is not overly large. http://Booking.com has done it multiple times in the past years and it worked well for them.
Having said all that, looking at your question, I do believe that you are asking the wrong questions, or I am completely misunderstanding your problem statement.
Short description: you could split your data in many parts and store ~50 part on each server. It will help you to avoid the second biggest problem of sharding - rebalancing. Just move some of them to the new server and everything will be fine :)
I strongly recommend you to buy it and read "mysql scaling" part.
Shard-Query is an OLAP based sharding solution for MySQL. It allows you to define a combination of sharded tables and unsharded tables. The unsharded tables (like lookup tables) are freely joinable to sharded tables, and sharded tables may be joined to each other as long as the tables are joined by the shard key (no cross shard or self joins that cross shard boundaries). Being an OLAP solution, Shard-Query usually has minimum response times of 100ms or less, even for simple queries so it will not work for OLTP. Shard-Query is designed for analyzing big data sets in parallel.
OLTP sharding solutions exist for MySQL as well. Closed source solutions include ScaleDB, DBShards. Open source OLTP solution include JetPants, Cubrid or Flock/Gizzard (Twitter infrastructure).
As of 2018, there seems to be a MySql-native solution to that. There are actually at least 2 - InnoDB Cluster and NDB Cluster(there is a commercial and a community version of it).
Since most people who use MySql community edition are more familiar with InnoDB engine, this is what should be explored as a first priority. It supports replication and partitioning/sharding out of the box and is based on MySql Router for different routing/load-balancing options.
The syntax for your tables creation would need to change, for example:
InnoDB foreign keys and MySQL partitioning are not compatible. Partitioned InnoDB tables cannot have foreign key references, nor can they have columns referenced by foreign keys. InnoDB tables which have or which are referenced by foreign keys cannot be partitioned.