So I always enjoy doing quick reviews of sites with situations like yours because it gives me insight into some issues I have on my own sites/projects that I'm just too close to see. The "distant nature" of reviewing someone else's site is sometimes that fresh perspective you need. Anyway, upon my poking around......
DISCLAIMER, if anything I say is wrong, it's either that I'm just wrong, or I didn't spend enough time looking into it because we're all very busy peeps (I'll claim it's the later)...
(1) Your Links VS. Theirs...
No arguing that you have more links than they do, but I suspect many of your links are from low quality blogs, I saw a bunch from directories that probably don't even pass strength anymore and so on. Without doing a full look through, links are hard to gauge. I didn't look at Sterlings in any detail, but I saw a few pretty decent links even though they have peanuts compared to yours in terms of quantity. So I'd say your link profile is definitely better, and it probably does help you more than theirs does, but obviously it's not enough.
(2) Your Content VS. Theirs...
This is where I think you're falling victim to being "too close". When I compare your content to theirs, I really don't see you as having better content. You have a bit more "descriptive" text than they do on product pages, but they have more "category-like" pages that has decent content on them (as do you). And to top it off, they have this "questions" section on each product page similar to a commenting system, where customers ask questions right on a product page, and Sterling staff members answer them right their on-page. So when I look at content comparisons, I see that as being a wash in terms of "quality" and they murder you in terms of quantity.
(3) HTML and technical "crap"...
When I compare your source code to theirs, theirs is definately cleaner, but it appears yours may be being compressed, which could be the only difference. I don't see any huge holes in that respect. Again though, I'm only glancing. But in my experience, you have to do some pretty dumb things in terms of your code structure with errors and what not to make that hurt you, which it doesn't seem you're doing. So I call this a wash also.
HOWEVER, when I'm on your main Velux Windows page, the content in your Welcome tab isn't viewable. The search engines don't care about that because it's included in your source, but I can't see past your 3rd paragraph in that area. I can see there is content below it, but the In a Loft Scenario and For Open Ceilings it gets cut off and I can't see the rest. That is likely hurting your conversions.
CONVERTING THE TRAFFIC YOU DO HAVE, IS OFTEN BETTER THAN GETTING NEW TRAFFIC, depending on the market you're in. I'm using the latest version of Chrome, but the problem is also present in IE10.
(4) Are you a CANNIBAL?
Now research this yourself, and don't put too much stock in what I'm about to say, but from a content perspective, is the way you're interlinking your so-called "helpful" content in a way that is actually hurting your ability to rank overall?
The pages that you have that you say are putting you above SterlingBuild in terms of content quality, is your linking to them from every product page causing you issues?
I see almost every product page within the category I looked at links to the Protect Velux From Snow and Ice and the Velux Product Codes Explained pages. I think this is something someone else touched on in response to me and my blog issues with our site. You're telling the google machine that these pages are uber-important because every single product page you deem them to be relevant to are linking to them.
If you check the SERPS and go deep all the way into pages 5 through 15, are you seeing these Video & Article pages ranking for terms that maybe are to "general" in scope for them? If so, it could be causing a loss of strength when it comes to your product pages ability to rank on their own.
I'm not sure on how I'd fix that though, or if it's even a legit issue. it's just something I'd chew on and maybe play around with. You have to ask yourself, does linking those articles from product pages like you do actually provide the customer with insight that may push them closer to a purchase? Even if it "could" be helpful, is anyone actually ever clicking on them?
Just a bit of insight. Hope it's helpful.