It might make one question the underlying assumption that competition somehow can cause people to somehow magically become better (a concept many people have which makes no sense). In reality, competition changes how people allocate resources as they play a strategy game to not lose control over segments of the market they perceive as strategically important. It also causes them to lose their negotiation power in the ecosystem, which can be good (as they can't push around smaller players) but also bad (as they can now be pushed around by larger players or loud users).
Mozilla used to be able to sit around and say "we absolutely refuse to do certain things, and we want to spend our time figuring out how to make the web an interesting place for power users and developers". I respected that Mozilla. It had a lot of clout in the market and used that clout to fight against DRM on behalf of all users while spending their resources building a super-extensible platform (which I think is a better description of Firefox's crazy plug-in oriented nature).
The post-Chrome reality is that Firefox no longer has an automatic dominating position in the "alternative" (non-IE) browser space, and so they have had to start caving to loud user demand and start fighting for the end-user market segment. They don't have the ability to fight against DRM anymore, so they have been forced to include Adobe DRM by default. They don't have the ability to waste a lot of time on power users anymore, so they are dropping all the complex-to-maintain parts of their platform spec and have started dumbing down the UI.
The one thing that Chrome did that was truly important was not to compete against Firefox: it was to prove to the world that something--specifically high-performance JavaScript--was both possible and desirable. This is the one positive aspect of "competition", and it is something that frankly should never need to happen in the world of open source, as one can do that in the context of the other project: I can't imagine a scenario where Firefox would have turned down performance patches :/.
But of course, Google isn't going to want to do that, because Google is a company with a strategic vision that happens to benefit from owning the web browser and being able to unilaterally make major decisions and perform weird experiments and crazy product integrations through it, which is all the easier for them to bootstrap as they can use their position as "the place almost all people both search and advertise" to push Chrome on people. This means that Chrome has no reason to collaborate with anyone, and even the one alliance they sort of had (with Apple on WebKit) they broke off when they decided they didn't have enough unilateral control: rather than collaborate as part of a community, Google just wants to own the product.
They also happen to be the primary customer of Firefox, so Mozilla is being forced to operate on smaller budgets. Note that this is the usual effect of competition and should be the obvious one: the idea of someone "stepping up their game" makes no sense when you are now operating on smaller margins (as competition means you can't demand as much share of the profit on any particular transaction) of a smaller market (as competition means that some customers will be using your competition). You only get to "step up your game" momentarily, often towards frustrating ends (such as giving up the DRM battle or trying to dumb down your UI as fast as possible), until your resources start to wither. (Yes: in a small initial market, competition can cause greater customer awareness leading to more pie for everyone; but that obviously isn't the case here: that is only true near the beginning of a new concept, when no one even believes the thing you are doing is relevant or valuable.)
In this case, it is even worse, as the primary customer to Mozilla's product was Google... and so they are essentially screwed in that negotiation. Firefox has had to switch to Yahoo as the default search engine and start making content deals to bundle marketing and software with their product, something they were morally opposed to doing in the past but have been forced into doing due to competition. This also doesn't come cheap with respect to executive time: rather than working out their product and platform vision, they are having to spend time negotiating and having painful conversations about how to keep their company from being destroyed and what morals they are willing to compromise for how long in order to maintain that fight. I don't particularly love Mozilla (as someone who has been paying attention to the open Internet since the beginning, I frankly found Netscape's business model of selling web browsers bundled with ISP contracts terrifying), but I have great sympathy for them these last few years, and absolutely do not see Chrome as being a positive force for anything at all in this ecosystem, except maybe security :/.