Here are a few impressions of the 5906 for you.
A few years ago, my Department wanted to standardize and went to the 5906. I was using a Sig 226 and loved it, but they were giving away brand new guns. So, I got one.
Being a long time fan of S&W 9mms, I found the 5906 to be a very fine shooting gun! It did everything very very well.
As time rolled on, it seemed to get heavier and heavier to the point of distraction. I, reluctantly, turned it in and returned to my lighter weight Sig.
I often thought how nice the 5903 would have been? What a great off duty gun, too!
In short, if you are only going to shoot it and not carry it, then the 5906 is a good choice. If you will be carrying it, the 5903 is so much better and it will shoot nearly as well for you.
For me, the 5903 is the ticket!!!!!!!!!
However, when all is said and done, you won't go wrong with either.
Hope this helps?
Good luck!
PS: Denver Dick's comment is well worth considering.