i perfer to do both. i like to do a 3-5 min walking warm-up, then a 10 min jog, then HIIT for 10-15 min then another 10 or so minute jog and 5 min walking cool down.
i agree with lady c 45 minutes of the same pace can get boring.
moderately difficult for 45 minutes would be a challenge I imagine for someone to maintain. That person would have to have a certain amount of conditioning to achieve that.
What is best for you depends on your goals and what it takes to motivate you. Doing something with lessor gains and slower returns is better than doing nothing at all.