Real Drummer Question

No it is not odd at all and in fact very common.  The cross stick in the verses will have a slightly softer sound and simply be emphasising the 2, 4 beat in a nice more subtle and relaxed way.  The fact you have asked means you probably feel the verses need to be a little less strong and the cross stick is the thing for doing it.
 
Snares in choruses add power and intensity to the choruses.  What I feel as a drummer though is quite often after one or two verses and some choruses I tend to stay on the snare for the later verses.  Usually because by the time you are half way the verses may have more going on in them and need a little more than the cross stick.  With real drums though it is easy to hold back and get a slightly softer and different snare sound in the later verses and then just by changing the stroke and power the choruses can have a slightly different and louder snare sound.   ie if you do stay on the verses with the snare try and find a way of still differentiating them.
 
Watch out recording and mixing the cross stick and the snare.  It is not hard to end up with the cross stick being louder in the verses than the snare in the choruses and you sort of need it the other way around.  During recording just adjust levels so you don't clip with either but I find in mixing I often need to pull the cross stick down a little in the verses and make the snare louder in the choruses to get things back to how it would sound live.

Thanks for the great answer! The verses are the story and the Chorus is "Oh Nancy" a few times, and then "Please let me love you. The rhythm guitar  verse part is a "nervous" arpeggio.
 
It lends itself to a busy chorus but I don't want busy drums and bass. I thnk we'll have the guitar do some response lines in the chorus..

I had problems with the link but it is fixed now. I'm gonna re-track the bass today.

Yup I hear it... COOLIO! and thanks!
 

Im a drumist too, and Jeff nailed the answer...