The Wire is very specifically about the whole war on drugs in the US and it influences almost everything within the show...
I don't think it is, imvho. There's a lot of references to it in the first 2-3 episodes of the first season but after that it fizzles out to be a procedural. The Wire is a bit up its own arse about being Not Just A Cop Show whereas The Shield isn't afraid to throw in the occasional explosion or gratuitous stripper. As it happens, I quite like procedurals so I like The Wire for that.
Where I think The Wire is better than the The Shield is in the character development/rounding out of the criminals/non-cops. The Shield is a bit like The Bill in that respect - the crims are just a rotating, interchangeable morass of people and you never really see the same person twice. Oh, it's the Biz Lats, oh, it's the 1-9ers. That's esp true in the later series.
Markus Degarian (the crazy Armenian) is really two-dimensional and we never learn much about where he (or any of the other Armenians, or the other crims) "come from". Antwon Mitchell is a bit more developed but even then it's still pop psychology [i wanted to insert spoilers here - what's the code?].
The same is true for the cops, especially in comparison to how e.g. Tony's crew is developed in The Sopranos. There's a lot in the first series about Julian and his conflicts, and in the series after there's more about Dutch and how work affects him, but we still don't, for instance, know what Vic did before he was a cop or why Gardocky seems to know everything technical. But we know much more about Paulie Walnuts, his army career, his imprisonment, his bizarre love life...
Also, I think The Shield changes remarkably in tone after the first two seasons, which I suspect is because you have so many more people writing it instead of just Shawn Ryan (who seems like a huge douchebag if you watch the DVD extras btw). Fun fact: Ryan claims that he wrote the whole first season on an epic bender listening to a Kid Rock album. Eventually the neighbours called the cops and he named Julian and Danny after the two cops that knocked on his door to tell him to STFU.