Either one should perform admirably regarding screen brightness.
Re: the stability issue, I've never heard any problems with a Kindle, and after years with one I've never had any either.
That is many peoples' experience with Kobo as well. But the Kobo firmware is said to be more unstable, and it depends a little bit on what you do with it. They are often fixing bugs and introducing new ones -- and most of each category may not even affect any particular person's usage.
Some people may suffer from serious stability issues, but some don't suffer at all.
Kindles never suffer (unless you ssh into it and start overwriting system files
which has happened but let's just say we know whose fault
that is).
In general, I'd say Kindles are good for the simplicity and just-read-it nature, and Kobo is better for customizability.