With most warranty companies you wont have a choice, you will get what they buy for you, unless you cash out and buy your own system, which I would recommend you do.
To answer your question though, Goodman in my opinion is a better unit, better cabinet and compressor than the Payne, that being said, proper installation is the key to any brand's performance and longevity
IMHO, your comparing two bottom of the barrel units. if i had to choose between those 2 I would take the goodman just because it think payne is about the ugliest unit i have seen in many years. Atleast the goodman has a casing around the coil to protect it
warranty companies use either of the 2 brands and the only bad thing about payne is the Bristol compressor. Goodmans cabinet doesnt fit correctly around the bottom. Gaps.
Either unit can work well with the right installer in charge of the job.