Is running every day better than going to the gym every day?
Running every day is a BAD idea. (I'm assuming that we're talking about running seriously, more than 10-20 minutes/day.) Running is a high-impact activity and your body needs time to recover. Running every day is a surefire way to develop overuse injuries.
It would be better to bike every day, since biking is not high impact, but you still need time to recover. I've managed to ride a bike for 30+ min daily for a month once. Lost 8 lbs and logged almost 900 miles, but, boy, was that exhausting.
Going to the gym every day is feasible but generally unnecessary, since it requires you to split exercises into groups. As a rule of thumb, you don't exercise the same muscle more frequently than once every 72 hours. This means that, if you want to do weights every day, you'd need to do, say, upper body and arms on day 1, torso on day 2 and legs on day 3. It would take you, literally, 15 minutes/day to do a full daily program. It's wasteful for most people and only the most experienced weightlifters/bodybuilders bother with that.
A better balanced approach for someone who's not already in excellent shape would involve gym twice a week, run/bike three times a week, and two off days.