i used to always give raw and have free flowing dried all the time (the dry was hardly touched), but a thread on the dog forums a while ago (i know i look like a noob but i'm not) had me investigating in depth into the ingredients... i did the same for the dry and now i dont feed dry.
I do give my cats the occasional wet food though, more because when i go away its easier for their temporary slaves to feed than raw is.
About the constipation... completely agree with spid on the pilchards in tomato sauce - works wonders!
As does salmon/crab/anchovies/tuna in olive oil!
beware if your using the olive oil one though it can be quite a clearout!
The only time my cats have suffered constipation is if ive overdone it on the raw bones... and a tin of pilchards between them soon sorts it out!
ooh meant to say too.... (for other people reading), remember without all the crap in the diet... the cats crap less, dont confuse that with real constipation!