The Samsung Galaxy S3 has a 32 GB model. They also have an SD card slot to increase the storage on them.
Regarding the screen brightness, the SGS3 at 100% brightness is roughly equivalent to an iPhone 5 at 50% brightness. I think the iPhone 4 is roughtly the same. I'm not sure how bright you normally set your phone to or what environment you normally use it in. I find that I don't have a problem with the brightness on my SGS3 most of the time. If you are outside on a bright sunny day, the SGS3 screen may be a little difficult to see. You may want to go to a store to check the brightness to see if you find it OK for your needs. I'm sure someone can load up a video for you.
The Note II is also another option. I'm not familiar with it though.