Just curious as to what Sitepoint members prefer from their clients with a pre-paid monthly budget vs hourly charging.

Perhaps I should point out that the type of clients are long-term where you will be working with them for 12 months minimum. I think definitely follow the KISS model for short term work.

Monthly Budget:
For -
potential to earn more per hour in a laid back month
easier to outsource/bring more people into the project
more decision making power to the developer in terms of how money should be spent
prepaid credit rather that postpaid compensation

Against -
potential to earn less per hour in a hectic month
more expectations and responsibility to produce results

Charge by hour:
For -
simple get-paid-for-what-you-do system
lots of hours means lots of money

Against -
easier to put tasks off indefinitely
a quiet month means you earn FA
$xx an hour sounds like more than $xxxx a month (doesn't it?)