Flexible is sort of 'flexible' and bends a lot, semi-rigid is more sort of 'rigid' and doesn't bend much.
I have always gone for flexible because you can bend it out of the way easier to get under boot floor, whereas rigid will have to be removed first. Flexible is not as easy to clean as it's not really washable as it tends to be like a 'thin sponge', so if you are to carry e.g. muddy boots, etc, go for rigid so you can easily wash it.