I love both shows. Both of them are real in a way that many other shows are not. I rarely feel like someone is being written out of or into trouble. Story arcs follow the natural outcomes of good or bad choices.
I loved The Shield, but in the latter seasons of the series, it became comical how Kurt Sutter and Co. would write characters into and out of trouble. Now he's done even worse on Sons of Anarchy. What they do on The Wire and Breaking Bad is much more subtle and believable.
The difference for me between the Wire and Breaking Bad is that I always felt that while The Wire's ensemble cast was fantastic, it was just an ensemble cast. No one actor was the standout throughout the series as Bryan Cranston has been on Breaking Bad. To me, that's what makes Breaking Bad special, similar to Tony Soprano on the Sopranos. I still think The Sopranos is probably the best show ever, with Tony Soprano the best character ever.
That said, Bryan Cranston and Michael Chiklis are probably my two favorite television actors. I didn't know enough of James Gandolfini to have any problems believing he could be a mob boss, but I would never have believed that Hal Wilkerson and the Commish could become Walter White and Vic Mackey.
For all of the crap music that's coming out right now, we're really lucky to be enjoying the current age of television. I can't remember when there have ever been this many great shows on at one time. It's impossible to keep follow all of them at the same time. Thank God for Netflix! Speaking of Netflix, Orange is the New Black is a great show if you haven't started watching it yet.