Bass: Dynaudio Confidence C2 vs Contour S5.4

I am cross-shopping the above speakers as an upgrade from my current C1. I prefer moving to full range speakers rather than trying to integrate a sub. Looking at the stated frequency ranges for the two speakers is interesting:

The Confidence is listed at 28Hz–25kHz and has two 6.5" drivers.

The Contour S5.4 is rated at 30Hz–27kHz and has two 8" woofers plus a 6" midrange.

Based on driver assortment it would seem that the 5.4s should have more slam and extension. Am I to believe that the C2s actually go deeper than 5.4s? The local dealer does not have both models in stock for a side by side.

Power will be via the new Bryston 4B SST squared. Again, I'm wanting to upgrade because I'm a closet basshead. The C1 is awesome in everything from the midbass up, but I can't help but feel like I'm missing something.

IMHO, you want the 5.4's if you are a closet basshead.
Can't speak for the S5.4's, but my during my stint with C2's I still needed a sub to get decent bass. If I were you, I'd either keep the C1's & add a good sub (REL Stadium, Aerial SW12, Velodyne DD15) or save up for Dyn C4's (assuming your room is large enough for C4's as they need room to breath), and you are able / willing to use room treatments. C4's are selling for surprisingly low prices on the Gon ($8,500 or so).
With proper amplification I find it unnecessary to integrate a subwoofer with the C2s. Dyns do not require a lot of power but they do excel with clean, high-current designs. (We just did a setup for a customer utilizing a Naim SuperNait and C2s with awesome results!) Burmester and Sim also work really well in unleashing the C2s full-potential.
I think it's somewhat dependent on room size. If your room is big enough, do as Pdreher suggests and save a bit longer and get a pair of C4's and you'll never look back. I had the C2's in a medium-sized room (14x18x8) and was satisfied with them as full-range speakers on a wide range of music. When I moved them to a large, open LR, I wasn't.

I've never heard the 5.4's. I would guess that, despite the measurements, they sound fuller in the bottom end, and if your room / music tastes required that, they'd be the better choice. Personally, I'd stay in the Confidence line.
As a C1 owner too I'm considering upgrading to the C2's for some more of that Dyn bass. Currently I have a Rel B3 and although it integrates well it just isn't that Dyn bass. I would say when I demoed the C2's in my home I got a lot more bass than the C1's but not quite enough. I think my problem is my room though. I seem to get great bass everywhere but the sweet spot. I do have to listen nearfield. Placing the sub in a corner really helped. Dyn's need room to sound their best. The C2's sound much better at my dealer than at my home partially due to his room size and he has better electronics. I have a Bryston B100 and your B4 squared should be plenty of good power. In my situation I'm not sure if I can live with them here without the sub (but the C2's sure do look better). In fact to make the C2's sound as good as the c1's for mid's and high end in my room I had to get them pretty close to the back wall and not toe them in as much.

I will admit I have never heard the contour line because once I heard the C1's I stopped my speaker shopping and had to have them. At that time my dealer did not have the C2's or C4's to compare but even so the C1's were way over my budget. I still haven't recovered from that yet either. To me the confidence line is fantastic in transparency imaging and detail.

Were you able to compare the 5.4's to C1's or the C2's at your dealer since he doesn't have both?
I think the step back you would take in the mids and treble would outweigh the benefit of the Contour s5.4s added bass.

The C2, C4 or Sapphire is your logical next step.

Just decide how much bass you want and go from there. Also maybe consider room treatments. After treating my demo room with ASC tube traps (I am an ASC and Dynaudio dealer btw) I found that the perceived bass actually sounded like it was playing lower than before the room was treated.
I guess another way of phrasing my question is: can the C2 really go down to its claimed 28Hz without significant rolloff? Any C2 owners able to corroborate the frequency ratings?

I've owned the C2's (28Hz) & now the C4's (27Hz). The difference in bass output is significantly more on the C4 than the 1Hz difference in the published specs. I think the 28Hz is somewhat deceiving, albeit not intentionally.
I've owned the Contour S5.4, C2 and C4. The bass on the C2 does go low but only if you feed them lots of power and turn the volume up past normal listening levels. At most listening levels I didn't think the C2 had enough bass. Save up for the C4