The mask helmet is there for protection and safety. Never make a decision on any safety equipment based on how cool it looks or what others are doing. Get the one that protects you the most. That would be the hockey style mask.
My son is in 9th grade and will be trying out for his HS team in the next few weeks. He has always used a hockey style mask since he started catching in LL 5-6 years ago. All the time he asks me about getting a traditional style and, inveitabely, the terms "cool" and "everyone's doing it" come out. You can imagine my response.
I played with the old school two piece myself and never played a game with the hockey style. I have caught some of my pitchers bullpens with the hockey style and I really like it to be honest. But the whole "cool" and "everyone's doing it" is generational. When the hockey style mask came out everyone wanted to have one because it was "cool" and "everyone's doing it" as well. Now that the hockey style is the norm the kids coming up see the old two piece as trendy. As the OP said each one has it's pros and cons I think for overall bang for the buck the hockey style provides more protection.