AlbertaBeef, Would a new intake be recommended, or is the stock circle intake adequate?
ok good question, about your 2003 1500, the model for your bike is VN1500E6
the factory stock MJ and PJ for your bike when new was,
138 MJ
45 PJ
Pilot mixture screw aluminum plug installed
When you bought the bike last april 2016, the previous owner rejetted the carb with V&H pipes and kept the airbox factory stock and you have the jetting receipt.
You are experiencing poor gas mileage of 12.5 km per litre which is low, with 15 km / litre being minimum you should be getting.
You also mention that your bike is having poor power, which corresponds to the low km/litre number, the culprit looks and appears to be the bike is too rich, which is causing the poor power and poor mpg.
rich = too much fuel to the amount of air intake
you asked if breathing more air would help and the answer is yes, if you leave the carb as it is now, letting the intake become less restrictive would help yes, but here are some comments I have doing that.
If you want to install an aftermarket intake (less restrictive), the gas tank has to come off and the carb removed and the cross-over tube from the left-side filter to right-side intake has to be cut out of there and removed. With an aftermarket intake, the carb jetting needs to be richened up, and given that even if the MJ and PJ in there now is perfect for a new aftermarket intake, you will need to remove the carb anyways to find out what the jetting currently is, unless that receipt from the previous owner has information on the jet sizes installed.
If you want to keep the intake as it currently is, and since the bike is running rich, to fix the poor mileage you will need to find out what size jets were installed and how many turns the pilot mixture screw was adjusted which means you will need to remove the carb anyways to find out.
Or you can decide to live with your present setup as is now, one thing I recommend is to use regular 87 octane fuel and not premium. You could also try a K&N filter and see how your power and mileage work out. The only risk to that would be you find out that with a new K&N you still have poor power and poor mileage and the expense of the K&N was of no help, but it might help, the only way to know is to try one. A new aftermarket air intake is also costly, and there is some work involved in that to install it and also carb work to get the jetting right.