Since I'm not a mathematician, the Kreimer-Connes work is hard for me to follow; below is only a statement of my understanding, not necessary the truth.
Disclaimer aside, the work of Kreimer-Connes has very little relevance for your average working physicist, at least at the moment. What they have done is to put the usual methods often used in HEP (i.e. tracking Feynman diagrams and coming up with suitable counterterms to cancel infinities) on a rigorous mathematical basis. Prior to that, it was not clear whether the procedures being used actually constituted a self-consistent set of rules. They show that it is, and in fact it is a sort of beefed up construction of a type that mathematicians have already known for a while. However, that "beefed up" part still means that they don't have any new ways (unknown to the physics community) for actually doing calculations. No doubt someday someone will exploit this fact and do something amazing, but right now that's not happening. In fact, I'd laid bets going the other way --- some heuristic, ad hoc procedure dreamt up by a physicist will get turned into a valuable theorem on the pure maths side first.
As such, the relation to the Wilson-Polchinski view is as usual for the HEP vs condensed matter points of view. At the end of the day, we have the fact that we need to measure some parameters. These are the "physical" ones. Our theory, on the other hand, deals with "bare" quantities, and it is up to us where we choose our cut-off. Changing the cut-off changes the precise relationship between bare and physical parameters. For some calculations it's easier to put the cut-offs very low, so that bare and physical parameters are almost the same. For others, it's better to put it high, and apply some combinatorial cleverness to cope with the diagrams.
The usual feeling is that the condensed matter view is clearer on what the various relationships are, but that the HEP methods are strictly more powerful. Specifically, it's hard to do momentum-shell renormalisation if you need Lorentz invariance. Gauge covariance only makes things worse. Whereas dimensional regularisation has the wonderful benefit of being an entirely orthogonal choice to any physical symmetry.
But really, where do you get to say the condensed matter view is clearer when Wilson was a HEP guy who "saved" the condensed matter field 
(ok, ok, Kadanoff should get a lot of credit too 
However, it's rather telling that HEP no longer uses the Wilsonian methods of momentum shell renormalisation --- it's hard to find a suitable shell if you have a Lorentzian metric. We squidgy stuff people are always working with a Wick rotated system, so we can. I don't consider the combinatorial counting of counterterms at each order to be particularly physical --- it's a very neat piece of mathematics which implements at the end the same thing, but is more abstracted from the system. Clearly I'm just not clever enough to cope with the extra step...
