Unless you're pressed for time to get to your destination, or you're really short of funds and the extra hundred bucks is a big deal, just bite the bullet and book the earlier flight with the longer connection. It has nothing to do with how long it takes to navigate the airport. Any airport can be crossed on foot in a 45-minute window, assuming you don't need to exit the secure area and be re-screened in the process.

But that only applies if you land on time. You never know when weather or IRROPs can add a half hour to your flight time. That's all it would take - a 30-minute delay to your takeoff from a storm on the other side of the country, or from a simple part replacement to your plane - and you'd be down to a 15-minute connection. If you take off 45 minutes or an hour late, then your connection is gone entirely.

Spending 3-4 hours in an airport is certainly not as much fun as a theme park, but DEN is a large enough place to get a decent meal, have a cup of coffee, use a bathroom that's bigger than a coffin, and relax for a while in a chair that doesn't have a stranger's body pressed up against yours like a lover. Three to four hours is enough time to go to any other terminal to seek dining or shopping options, or even to exit the secure area. With only 3-4 hours I wouldn't risk leaving the airport entirely, though.

Looking at DEN's web site, there appear to be multiple lounges, and multiple outdoor observation decks, where you can relax, read, and stretch out for a while during the wait.

Look on this as an opportunity, rather than a problem.