By "can't keep up", I assume you mean the pressure drops below the 90 psi regulated pressure normally used for air tools. If that's the case, then the diameter of that air line is unlikely to be the issue. If you're using a 3/8" air hose from your tank to your tool, there's much more pressure drop in the hose than in the short compressor-tank connection.
Consumer-grade compressors are notoriously overrated. A true 6.5 hp air compressor will draw close to 30 amps at rated pressure and CFM. There is a reason Coleman only used a 3/8" line: that's all it needed.