Personally I have taken the red cross first aid courses and found them to be basically useless, apply pressure and rush to call 911, which is about as useless as tits on a boar hog when you are 3 days from the trail head.
I took a NOLS WMI WFR (National Outdoor Leadership School Wilderness Medical Institute
Wilderness First Responder) course a couple of years ago, and it was great. I learned so much from it it was ridiculous. Now for me that is saying a lot, my older brother is a paramedic so I know a lot from him plus all of my years in Boy Scouts and injuring myself and just being alive. Their course really teaches you what to do through class room and hands on teaching, with lots and lots and LOTS of scenarios where you switch off with people being the victim. They actually taught us wilderness protocols so when you actually need to fix somebody and your sat phone is dead and you can't call 911, you don't have to watch your buddy die. One of my favorite parts of the class was the improvisation. They actually taught us how to use the stuff we already had on us to fix people, backpack stays for braces and sweatshirts for C collars. Very useful if you don't plan on packing a hospital in your FAK.
I cannot recommend this class highly enough, I feel it is a must for people who actually spend time out in the woods doing the things that we do. They also have other courses, like Wilderness First Aid and Wilderness EMT for those that are looking for more or less instruction.
Lastly I would like to say that NOLS is not the only place to take a course like this but when you are looking for something like this make sure it is Legit. There are a lot of people teaching WFR courses out of their church and who don't have any real credentials. Now I do recommend this over nothing, I would really try and get a class that is sanctioned by the Wilderness Medical Society as they keep up on what is being taught and any advancements in the field.