This is a discussion that we had at ACSC "once upon a time."
In the end, we concluded that it was a subjective question. The navy...okay, it's a highly impressive force projection vehicle. Think about it...you're a belligerent government with an ocean coastline. You're causing problems and the global community is talking tough. You laugh. Then you wakeup one morning to learn there's a carrier battle group parked nearby...force projection.
That being said, I do not believe you will ever see a classic sea battle (to include crossing the T) again. I think fleets will be relegated to the role described: force projection. That and disaster relief. I laughed when I heard that at ACSC until a navy SWO said "have you any idea of the humanitarian relief capacity of a CVN? FYI, for those not familiar with navy terms a CVN is a nuclear powered aircraft carrier. I was one that did NOT know. He then told me. I was stunned. Picture a carrier in a harbor of a location devastated by natural disaster; the people have no fresh water or medical support. Bring in the carrier...if memory serves, they can produce almost 200k gallons of drinking water a day. And medical support? They have multiple operating theaters, full medical staffs that can handle pretty much anything, a large galley (food in a crisis) as well as transporting helo's, etc...etc. VERY impressive. And it's not just the carriers that can do this. This is just a little that I recall from the discussions we had.
The army. Face it, in a combat situation where the objective is to defeat an enemy and take/occupy/liberate the land, you MUST have boots on the ground. That means the army. The marines are a great "temporary" strike force, they're mobile, agile, and just good. However, they're too small. The army is large, mobile, diverse in combat power, and very integrated into the combat force. I had the chance to spend some time with an army unit and was able to observe what they do. I would not want to do what they do; the land battlefield is a highly dangerous area. And they are there, all the time, every time, and ready to go. My hats off to them. They are a "in your face" force projection tool. They also have the ability to convert to a humanitarian force, bringing in all manner of support to disaster areas.
So which is more important? I actually think both are. I use my first war, Desert Storm, as an example. I flew USAF jets. I got to the AOR via a lot of air refueling (and a very sore rear). The air bridge was critical. Airlifters were able to move troops, equipment, and supplies very quickly to establish a "beachhead" until the navy could bring the bulk of EVERYTHING over on their ships. Airlift is amazing but let's face it, the navy can carry a WHOLE lot more at one time and deliver it. They brought in everything. They also brought in airpower. The army? They brought the land battle force that ended the war. The marines brought in the quick strike "we're not here, and then we are" impact force.
And I'm reaching the end of a long posting and the conclusion I've reached is the same we did then: the truly unified force we have is a combined arms force that works together, in harmony (except at the bar), to bring about success in our endeavors.
Too much?