Assuming you know the checksum of a seed. How much does the brute-force difficulty decrease? By 27^3, or more?
The checksum of an IOTA address or seed is formed by hashing that value and then using 9 trytes (or 3 in the case of the wallet seed) of the hashed value. Meanwhile, generating an address from a seed requires several hundreds of hashes.
Insofar as you are trying to discover a particular seed via brute force, knowing the checksum will allow you to discard candidate seeds more quickly because you won't need to generate addresses from them if the checksum doesn't match. In general, this will indeed occur 27^3 or about 20,000 times for each valid checksum. Taking a single hashing as an elemental operation, the computational speedup from this will be approximately the number of hashes required to generate an address divided by the number of hashes required to generate a checksum.
However, in practice, so long as preimage resistance of the hash function holds, knowing a checksum will not really help you at all. There are still 27^81/27^3 = 27^78 seeds with the same checksum as yours.