MySQL Partitioning: Is there a performance tradeoff between number of partitions and size of each partition?
Let's compare them
PARTITION SIZE
If you have the following:

100 million rows in a table
BTREE indexing
Each Page in the BTREE holds 1024 keys

What would the metrics look like?
Since LOG(100000000)/LOG(2) = 26.575424759099, a BTREE index with 1024 keys per page treenode would have a tree height of only 3 (CEILING(LOG(100000000)/LOG(1024))). With only three pages nodes, a binary search for the needed key in each accessed treenode would result in a pruning and isolating of about 30 keys.
NUMBER OF PARTITIONS
If you have the following:

100 million rows in a table
BTREE indexing
Each Page in the BTREE holds 1024 keys
You create 1024 parititions

The numbers would be slightly different.
Each partition should have about 97656 rows. What would the metrics become now?
Since LOG(97656)/LOG(2) = 16.575421065795, a BTREE index with 1024 keys per page treenode would have a tree height of only 2 (CEILING(LOG(97656)/LOG(1024))). With only two pages nodes, a binary search for the needed key in each accessed treenode would result in a pruning and isolating of about 20 keys.
CONCLUSION
Spreading out the keys just removes one tree level but essentially creates 1024 indexes. The queries won't know the difference. The search time would probably be nominal at best in favor of partitions. However, make sure all the data is active. Otheriwse, you may be hitting just a few partitions, while other partitions with rarely-accessed data just takes up space and are never accessed frequently enough to justify the partitioning. You may have different performance metrics to worry about that are more blatent (such as internal defragmentation in XFS, ext3 vs ext4, etc.) You also need to worry about which storage engine you are using because:

InnoDB indexing would be a little messier in comparison to MyISAM because of having to manage a clustered index
InnoDB does double writing of data in ibdata1 as well as the current log file (ib_logfile0 or ib_logfile1)