Is it just as difficult to find a desired output in a hash digest, for MSB vs LSB? This question comes to mind after seeing "custom" Bitcoin addresses with some special string at the beginning of the address. They are generated in the same way Bitcoins are "mined", continually hashing with a nonce + password to get some desired output. 

My question is, is it just as hard to find [HLOWRLD]M9VveeBLcY4UC4vjpPs6rZtFBQE as it is to find 1FpUYCpM9V[HLOWRLD]4UC4vjpPs6rZtFBQE as it is to find 1FpUYCpM9VveeBLcY4UC4vjpPs6[HLOWRLD]? *Note the values in the digest not in brackets can be any value

The reverse to the question, given you have some insane computer, would it be easier to try to find the input for [HLOWRLD]M9VveeBLcY4UC4vjpPs6rZtFBQE versus 1FpUYCpM9V[HLOWRLD]4UC4vjpPs6rZtFBQE versus 1FpUYCpM9VveeBLcY4UC4vjpPs6[HLOWRLD]?
As the other answers point out, output bits of a good hash function are uniformly distributed, so your substring has equal chance to appear in any part of the hash digest.

However, in the case of Bitcoin, the address is not a random string. Not only it starts with a predefined number (1 or 3), but the string is the result of the Base58-conversion, which may (I did not check) produce biased outputs. The addresses may even be of different lengths.