I'm not saying you should be blind to what is happening in your market, but I'm a strong believer that you should focus on making your product the best for your users that you can, and try to ignore a lot of the noise out there. Do what you do and do it really well.
FWIW: I think this applies more for smaller startups, and less for giant brands who are wielding and fighting against 100 million dollar marketing budgets.
What better way to make your product better for your users than to improve on things your competitors don't do well? I think that despite size, good strategic business thinking should always take into account the competition.
Actually Competitious has evolved into RivalMap http://www.rivalmap.com/ - I've used both at two different startups, and I found them to be useful, but not earth-shatteringly good.
In fact, I generally think that a minimum of time should be spent considering your competition (at least when you are a startup). Perhaps you set aside a few hours each month to review their progress, compare it to yours, identify features or strategies you will "borrow" from them (ie "fast follower" strategy), and consider what they'll be doing in the future that you need to respond to, or get ahead of.
Then, add those items to you action plan, and forget about your competition for the next month - focus on building YOUR business instead.
Just my $0.02 from the startups I've founded, funded, and grown.
There's also good ol' elbow grease, you could hire a programmer to data mine / scrape a competitors site to gather numbers and etc, if the information is publically listed.
But depending on the biz you're up against it might not be useful, i.e. you might need to keep an eye on who and how they're marketing themselves.
FWIW: I think this applies more for smaller startups, and less for giant brands who are wielding and fighting against 100 million dollar marketing budgets.