InnoDB offers:
ACID transactions
row-level locking
foreign key constraints
automatic crash recovery
table compression (read/write)
spatial data types (no spatial indexes)
In InnoDB all data in a row except for TEXT and BLOB can occupy 8,000 bytes at most. No full text indexing is available for InnoDB. In InnoDB the COUNT(*)s (when WHERE, GROUP BY, or JOIN is not used) execute slower than in MyISAM because the row count is not stored internally. InnoDB stores both data and indexes in one file. InnoDB uses a buffer pool to cache both data and indexes.
MyISAM offers:
fast COUNT(*)s (when WHERE, GROUP BY, or JOIN is not used)
full text indexing
smaller disk footprint
very high table compression (read only)
spatial data types and indexes (R-tree)
MyISAM has table-level locking, but no row-level locking. No transactions. No automatic crash recovery, but it does offer repair table functionality. No foreign key constraints. MyISAM tables are generally more compact in size on disk when compared to InnoDB tables. MyISAM tables could be further highly reduced in size by compressing with myisampack if needed, but become read-only. MyISAM stores indexes in one file and data in another. MyISAM uses key buffers for caching indexes and leaves the data caching management to the operating system.
Overall I would recommend InnoDB for most purposes and MyISAM for specialized uses only. InnoDB is now the default engine in new MySQL versions.