The good news is that you're both right! This is a very common question, as people are often concerned about whether one mode of activity done before another may help with greater weight loss, cardiovascular function, or more significant strength gains. To date there is no concrete scientific evidence to show that the order in which cardiovascular and strength training are done in a workout session has any impact on overall health and fitness. Any advice or recommendations of the benefits of one order of training versus or another is usually based on anecdotal reports and personal experience (except in the case of elite athletes who have very specific performance goals).
Your personal preference and the order that makes your workout most enjoyable are your best guide. You might consider alternating the order you do cardiovascular and strength training over time for variety. This is the method we currently use in our exercise studies at Tufts University to be sure that both components are emphasized equally. Keep in mind that no matter what order you do the exercises in, you should always warm-up slowly to get your muscles ready to exercise safely as well as cool-down by slowly bringing your heart rate back to normal and stretch your muscles to help reduce injuries.