The current Civic Si is, by all accounts, one of the sportiest-handling FWD cars on the market today. The Mini Cooper may be more agile, but that's it as far as I know. Sure, the Si completely lacks torque (especially compared to the firebreathing Mazdaspeed3), but it's rev-happy engine, light weight, and razor-sharp handling make it sportier than any version of the Mazda3, in my mind. The MS3 is awesome, of course, but I don't see it as quite as narrowly focused on pure sport as the Si is.
Also, in terms of Honda's sportiness, what about the S2000? By all accounts, it's sharper than the MX-5, though less well-rounded. [edit: I just remembered that the price gap between a well-equipped MX-5 and the S2000 is much larger in Canada than the States, so this might not be a fair comparison).
I agree, though, that in some areas, Mazda is sportier. The CX-7 is far, far sportier than a CR-V (and comparisons to the RDX aren't fair because of the huge price gap). The Mazdaspeed6 versus the Accord V6 6MT? No contest, the Mazda is worlds sportier.
Ahh... but you (and Dave, and others) are missing the point here. It's not about comparing Honda Model X to Mazda Model Y to determine which is sportier... it's the fact that Mazda lives up to its marketing hype about putting "Zoom Zoom" in every vehicle they make (again, I offer this position with the exclusion of the rebadged Ford trucks). Whether you prefer a flimsy, light clutch and over-boosted steering (Honda

) or kick-in-the-pants turbo boost (Mazda), the fact is that each of Mazda's automobiles have a strong element of driver enjoyment built-in. With Honda, this is not so. Pointing out the Si model doesn't mean all Hondas are sporty and fun to drive.
If Honda was really concerned about maintaining a sporty edge to the consumers' perceptions of their products (the way Mazda is), they'd want to have a competitor that not only meets the standards of the industry (ie. Si, versus GTI, SS SC, MS3... does it really excel at anything against the competitors?) but strives to exceed them. It's the competitive nature that's borne out of real die-hard auto nuts that obviously worked on the SS SC, SRT cars or Mazdaspeed's division.
Honda has one sports car. And while I'll be the first to admit that it's an absolutely lust-worthy machine, it's in the last year of its life now isn't it? Then what? And don't even get me started on comparing an S to an MX-5. Consider what $15,000 worth of parts can do to an MX-5 (the difference in cost between a top of the line GT model MX-5 versus the base price of an S2000). Would I rather have an S2000? Sure, but they're leagues apart in terms of price.