Which is better in the military and which gives you more opportunities in the civilian side, 68W or Hospital Corpsman?

You're looking at it all wrong. Army or Navy is the question you need to ask yourself. Both will give you nothing more than a Basic EMT cert and both will open doors to other medical fields. But neither will directly translate to a significant medical career field in the civilian sector after the military

Great question. It depends on what you want out of it and your goals. A 68W is a Combat Medic, and in the Army, any enlisted medical personnel will go to basic training and then to their AIT (Advanced Individual Training) to learn their specific role. So in this case, a 68W while go to Combat Medic school in Fort Sam Houston, TX. I am not in the Army, so I don’t know much about the MOS’s advanced fields, but I do know that 68W allows you to obtain your National Registry EMT Basic, which transfers well to the civilian side.
Now, the Navy is a little different. HMs attend A School after boot camp, which is our version of AIT. There are many specialties within the HM community, but every Corpsman completes HM Basic (A School), which is about a 4 month process. You are taught a broad range of skills that merge into a hybrid of anywhere from a nursing assistant to a paramedic or nurse. After completing A School, you will have the opportunity to specialize throughout your career and attend what is called a C School. We have many specialties ranging from Surgical Tech, Respiratory Tech, Cardiovascular Tech, to more combat/special ops specialties like Fleet Marine Force Corpsmen (green side that are embedded with Marines), Dive Med Techs, Marine Recon, and what’s called an Independent Duty Corpsman (IDC). IDCs are usually E-5 and above, and are essentially trained as PAs that can work independently of a provider and prescribe medicine and treat patients at a very high level, and are considered providers. We no longer offer Corpsmen the opportunity to earn their NREMT in A School, but you are eligible to challenge the exam. Specialties come with certifications as well.
I personally prefer the Navy because we are very adaptable to any given situation. All Corpsmen are basically trained, therefore we are one of the most sought out medical communities of all branches, as well as one of the most decorated. This means that if I were a Surgical Tech, I would still have the basic knowledge base to function outside of my specialty, which happens more often than not. This is different than the Army, who I have had the privilege of working with in the past. Their 68C (LPN) are limited to their scope, and are of no use in situations requiring skills above their scope, as Corpsmen have the ability to do much more. The same goes with the 68W, who essentially becomes limited to the scope of an EMT-Basic, which is also of no use in certain situations requiring more advanced or nursing care.
That’s just my take. Both offer great opportunities for experience. If you have a specific goal or just want certifications, maybe Army is your best bet. But if you want to be well-rounded and learn skills from every angle, go Corpsman.

HM is the biggest job field in the Navy. 45 K strong and over manned at 127% when I was in. If your intention is to stay for 20 years and retire. I recommend that you talk to your recruiter and pick anther job field. Or join the Army as a 68W. I was also an Army Medic in the Reserve and to be honest it sucked for me because I could not treat patients like I did when I was in the Navy. Pick wisely. I would not change what I did while I was in and have missed it very much since I got out. Respectfully HM2