I always had my suspicions about this, and finally got around to testing it. It would appear that Redguards get a bonus to hit and damage with bows and NOT melee weapons, while Woodelves get a bonus to hit and damage with melee weapons and NOT bows.

I rolled a woodelf sorcerer. I gained some levels, then broke into a house to use the "monsters spawn instantly when you sleep in a house" trick to level up to 15. I purchased an Ebony War Ax (damage 7-17) and an Ebony Long Bow of Luck (damage 7-17, +10 Luck). STR is 58, AGI is 100. Luck is 50 (+10 with bow equipped).

I then slept in a house until I had an Ice Golem spawn. I saved the game in multiple slots without retaliating. Went into ArenaEditor and changed one woodelf save into a redguard, and another into a khajiit. Went back into Arena.

The woodelf, with the bow equipped, would take 15-23 bow attacks to bring down the ice golem, or 12-16 with the war ax. Meanwhile, the redguard would take 15-23 ax attacks, but 12-16 bow attacks. The khajiit always took 15-23 attacks regardless of weapon. Probably killed it close to 20 times with each weapon for both the redguard and woodelf, and 10 times with each weapon for the khajiit.

Cannot confirm how this works with other weapons. It could be that the weapons used in this test are flagged incorrectly, but I selected them because they have the same damage values, can damage ice golems, and wouldn't break while I was levelling to 15. All characters had the same stats since they were edited from the same woodelf. Ice golems, like most monsters, have variable health, which is why I waited for one to spawn before saving and editing character race, to ensure that each character was fighting the SAME ice golem.

Just sharing this, as I see a lot of advice advocating Redguards for melee classes. This SHOULD be good advice, but I have my doubts after this test.