Yep, here's how you tell the difference:
1.) Look at the back of your crayfish...
Where the shell comes together, it's almost touching on P. clarkii (sometimes it is touching) and on a P. alleni there's a wide gap between it.
2.) Using those same pictures above, look at the claws. P. clarkii have very thorny and bumpy claws. And while P. alleni will get a little bumpy as an adult, it's much more pronounced on P. clarkii.
3.) Using those same pictures above, look at the body in general. P. clarkii has little raised dots all over it , whereas P. alleni doesn't (generally the spotting in P. alleni, usually seen in the colored versions, is just patterning. You can actually feel the bumps on a P. clarkii)
(Pictures borrowed from bluecrayfish.com - Big Vine)