Would it be OK if I told you it just depended on who you talked to? I did not think so. How about I break down the schools of thought on whether it is better before or after and how it really depends on your ultimate goals.
The Best Option For Your Situation: Like I said before, customization is the only way to reach your goals in the most efficient way. Below I've listed some of the most common goals of exercise routines and the most effective way to build your cardiovascular and strength programs to help you succeed.
1. If you are trying to gain pure hypertrophy (or muscle size) then performing a cardiovascular training session before your strength training could drain some of the energy from body. When trying to put on size, it is mandatory that your muscles have plenty of stored energy in them to perform a lift. I would suggest getting your strength training done first and then doing a very short (15 minute tops) extremely intensive cardiovascular session. This will focus on exhausting your fast twitch muscles (The bigger ones) and still give your body the cardiovascular benefits you are seeking.
2. If you are a cardiovascular buff like those who take off and run 5 or 6 miles every other day then I would suggest getting a light strength training program in before your run or splitting your workout sessions so that you perform either your cardiovascular or strength training program in the morning and another session in the evening. DO NOT skip on the strength training just because you enjoy cardiovascular training more. Strength training stabilizes your joints and lowers your chance of injury.
3. If you are looking to drop a few pounds then efficiency is your ultimate goal. Depending on your current condition I would suggest combining both cardiovascular and strength training together in what is known as “circuit training.” This is done by combining several strength exercises done back to back with very little rest in between. The reason that this works so well is that you will get your heart rate up into the rafters, increase your muscle strength and size which in turn will increase your metabolic rate. Think of it this way, cardiovascular training is a lot like putting money into a checking account, it's great to put all those calories in the bank but you do not get much of a return through interest. Strength training is like putting your money into a high yield savings account turning 12%. You put the initial calories in there and they continue accumulating until you are a calorie burning machine.
4. If you are just looking to maintain what you have then I say do whatever you enjoy. There is no real harm in putting cardiovascular before strength or vice-verse. As long as you are sure to get both of them done on a frequent basis then you are doing a great job.
I hope that this help put some perspective to why some people say cardiovascular ahead strength and the other way around. Keep in mind that these are just suggestions made from a trainer and I want you to be sure to keep up a routine whenever you head my advise or not. I hope that the information makes sense and is practical for your situation, and if you ever have a question be sure to email me at firstname.lastname@example.org and I'd be more than happy to help you out.
If you are interested in using the program that I helped create and use everyday then go to http://www.therpmsystem.com and put in the code: 376255532 to try it absolutely free for one week.