As a FFL, I will say that it doesn't matter. The story referenced above about the CR vs Cir. really shouldn't make a difference to the FFL. The FFL doesn't keep a copy of your license, nor does it keep a copy of your CHL. You have to show the FFL that you have a Texas residence (DL), and then the NICS is eliminated because of the CHL. A minor wording, like not having 'Ave.' would not be an issue with us. And, plus, how is anyone who could get the FFL in 'trouble' (ATF) going to know that there was a minor difference between the two types of ID? My personal opinion is that the FFL went overboard when it gave the CHLer a hard time.
So, long answer short, no, it shouldn't make any difference.
TBM