In spoken English, there is very little difference. It wouldn't sound strange to use either.
However, grammatically there is a slight difference between these two adjectives.
"Inspirational" demonstrates intent. We can talk about inspirational posters, inspirational speakers, or inspirational films. All of these things have a goal to inspire people. Maybe an inspirational poster seems cheesy or lame to you, and has no effect. It is still an inspirational poster.
"Inspiring" is related to effect. A sunset can be inspiring to you if you are an artist. Your hero can be inspiring to your life. These things are not necessarily trying to inspire you, but you can still feel inspired by them.
I hope that this was clear and helpful!