Just pointing out that not using a mouse is probably not this guys problem.
Yah.... mouse aim is unquestionably faster and more accurate, this was proven in Shadowrun which was 360/PC x-platform online MP.... but that REALLY only comes into play in fast paced FPS where headshots make a difference. Location of hit matters not in Skyrim, so the extra precision is unnecessary... and even then, I still pepper enemies heads with arrows more than anything else anyways. It doesn't take an obscene amount of skill with gamepad to reliably put arrows on target in Skyrim.
The biggest advantage to k/m in skyrim, besides console commands & mod support of course, is key bindings to equipment.... PC gets 4x as many quick maps.
Mouse vs anolog aim is more up to preference, familiarity, and comfort.... and it's generally well agreed as well anolog > WASD for movement as well.
OP just needs a better bow, a follower to tank for him, and/or to utilize sneaking.
Archery is one of the strongest & most reliable forms of attack actually.

