+0
Hi,

How are they different?

Thank you for providing us something.
Thank you for providing us with something.
Comments 
Hi,
They sound pretty similar to me.

Clive
AnonymousHi,

How are they different?

Thank you for providing us something.
Thank you for providing us with something.

In BrE, it should be '... providing us with something'. Maybe it is different in AmE.