This is context dependent, but assuming you just generally want to get in shape I would let preference decide this. Consider that doing them on the same day means that whatever one you do second, you may not perform it optimally due to being tired from the first.

If one were to do both in the same day I would choose the order based on goals. The one you do first will likely be performed better.

I would always balance out goals with lifestyle/preference in this regard. If you're trying to push the extremes of fitness or you have specific performance metrics that extend beyond "I want to get in shape and look good" then you certainly may be better off doing them separately, but that context can't be ignored. For many people, doing them together is more convenient, might improve adherence, etc.

These are things that need to be weighed out, IMO.

This is context dependent, but assuming you just generally want to get in shape I would let preference decide this. Consider that doing them on the same day means that whatever one you do second, you may not perform it optimally due to being tired from the first.

If you're going to do both, is there some sort of benefit on each side over doing one before the other?

OP: Personally I do cardio and then strength. My reasoning is I am not running marathons and I need to warm up somehow. I just prefer doing light cardio first compared to a couple lighter set of weights since it personally makes me feel better (my bones click, they click less if I move everything around for a while first). If your goals are to be really excellent at both I wouldn't do both the same day, one of them well suffer for sure.

As SideSteel mentioned, the one that you do second may 'suffer' as you are tired after doing the first. Not that I actually do cardio, but if I did, if I did them in the same session as lifting, it would come second as my lifting sessions are a priority for me and I do not want to be tired, especially when I have a sh!it ton of weight over my chest or on my back.

You need to warm up before strength training, but I do not consider a short warm up on the elliptical cardio.

Purely anecdotal, but I jogged (up hill) to the gym one day last week, and proceeded to have one of the worst lifting sessions I've had. Had to reduce weight on pretty much everything I did.

I'll not be doing that again.

Usually I do cardio and lifting on separate days, and warm up with a brisk walk on the treadmill, or five minutes on the elliptical.

I usually do 3 days of strength.

I do 5 minutes on my rower (the good fan belt one) to warm up. Is that ok? My hubby said when he was using a training he did 500m on the rower to warm up. I do more than that.

As long as your warmup isn't significantly effecting your ability to lift then I don't see a reason why you can't continue doing it.