My at home gym is now pretty much complete. I have lots of choices when it comes to free weights and strength training equipment: Ybells, steel maces, kettlebells, medicine/slam balls, heavy wooden mudgar/karlakattai clubs, Equalizer bars, chin-up doorframe grips, resistance bands, and more. Even a bowling ball!
For cardio my primary tools are a rebounder trampoline and a slide board. I also have a jump rope and an aerobic stepper, and I take regular walks of 2 to 4 miles in length. These walks are dog walks averaging about 25 minutes per mile, so I don't know how "cardio" they are but they are something.
Anyway, I like to do slide board before strength training. On the days I do slide board, I do it first thing in the morning, after a few minutes of stretching out and loosening up. I start out with an upright slide at a moderate pace and then gradually increase the intensity/speed in more of a hinged position. After 20 minutes on the slide board I do find that my energy when I switch to strength training is slightly more depleted than if I hadn't done the cardio beforehand. But that's no biggie.
Conversely, on other days I like to bounce on my rebounder mini-trampoline after doing strength training. The main reason for this is because after 20+ minutes of weights my body is very loose and limber and following that accomplishment with some trampoline fun is a good way to end a workout session. Also, early on when I first started rebounding the jumping would sometimes lead to a slight pain at the base of my neck, almost like a mild headache. This hasn't happened recently and does not occur when I do the trampoline after having already done some type of strength training workout.
You won't really find an answer to the question posed in the post title and that's because I don't know the answer. Each method has its pros and cons. By alternating cardio + weights one day followed by weights + cardio the next day I feel like I have the bases covered.