Hyatt changed their Best Rate Guarantee process last year, in that you now have to complete an online form and submit a screen shot of the lower rate found on another website. You still get 20% off the length of your stay however.
Hyatt further guarantees that a response will be made in less than 24 hours with their decision.
Prior to the online form, to file a Best Rate Guarantee you needed to call into Hyatt and then do the process over the phone. Although it was great on one hand in that you could get an immediate response, it appeared as though Hyatt blocked their associates from accessing many websites that are used for Best Rate Guarantees thereby making claims somewhat fruitless.
I have found that Marriott has the most lenient Best Rate Guarantee out of the major chains that I normally stay, with Starwood being the second easiest. Hyatt seems to be the most challenging, however it was somewhat dependent on the associate you spoke with prior to last year.
I recently filed for a Best Rate Guarantee for an upcoming stay. I was somewhat surprised when my claim actually got accepted. I did not make a reservation prior to filing the claim, but an email notification simply stated to call and provide my confirmation number once the booking was made.
Although it can take some work, having successful Best Rate Guarantees can save a lot of money during a vacation or any trip.