Note that I made this mod for personal use, and it is balanced for my load order and tailored to what I think fits the different races.

The Bonuses:

Warrior Race - Nord and Redguard
Magicka Bonus 0.5x INT
50 Attack
Combat Focus - Khajiit and Orsimer
Magicka Bonus 0.6x INT
40 Attack
Balanced Physiology - Argonian, Bosmer, and Imperial
Magicka Bonus 0.7x INT
30 Attack
Spellblade - Dunmer
Magicka Bonus 0.8x INT
20 Attack
Magical Ancestry - Breton
Magicka Bonus 0.9x INT
10 Attack
Manawell - Altmer
Magicka Bonus 1.5x INT
No Attack Bonus

These base bonuses mean that races are more versatile out of the gate, so a Nord frost mage who still uses Axes and Long blades for instance is a lot more viable.

Skills:

I changed skill allocation significantly, now all races have 6 skill increases, 3 skills with a +5, 2 skills with a +10, and 1 skill with a +15, for a total pool of 50 skill points.  I have also removed bonuses to Armor skills on all races except for Orc, who have a bonus to Medium Armor, and Altmer with a bonus to Unarmored.  I felt that races having armor bonuses ended up throttling a lot of them, and some races like Nord, Imperial, and Dunmer have a multitude of racial armors of different types, but only one armor type bonus.  Magical skills are also more evenly spread out amongst the races, with Nords and Redguards being the only ones without any bonuses to a magic skill.

I will now go over the skills by specialization, in alphabetical order.

Combat:
Armorer: Orsimer +15, Nord +5, Redguard +5
Athletics: Nord +15, Redguard +10
Axe: Nord +10, Orsimer +10
Block: Imperial +10, Orsimer +10, Nord +5
Blunt Weapons: Orsimer +5
Heavy Armor: N/A
Long Blade: Redguard +15, Nord +10, Imperial +5
Medium Armor: Orsimer +10
Spear: Argonian +15, Redguard +5, Nord +5

Magic:
Alchemy: Argonian +10, Dunmer +5
Alteration: Altmer +15, Breton +5, Bosmer +10
Conjuration: Breton +10, Dunmer +10
Destruction: Dunmer +15, Altmer +10, Argonian +5
Enchant: Breton +15, Altmer +5, Orsimer +5
Illusion: Altmer +10, Khajiit +5
Mysticism: Dunmer +10, Breton +5
Restoration: Breton +10, Imperial +5
Unarmored: Altmer +5

Stealth:
Acrobatics: Khajiit +15, Redguard +5, Bosmer +10
Hand to Hand: Khajiit +10, Argonian +5
Light Armor: N/A
Marksman: Bosmer +15, Dunmer +5, Redguard +5
Mercantile: Imperial +15, Khajiit +5
Security: Khajiit +5, Bosmer +5, Argonian +5
Short Blade: Dunmer +10, Imperial +5, Bosmer +5
Sneak: Khajiit +10, Bosmer +5, Argonian +10
Speechcraft: Breton +5, Imperial +10, Altmer +5

Attributes: 

Attributes aren't super different except for being a bit more standardized and the overall pool being 10 points larger than normal.  As much as I want to go into detail on the racial attributes here, it would create a ton of clutter.  Races now have 2 Attributes at 30, 2 Attributes at 50 (except for Altmer, who have 60 INT and none at 50), and the rest at 40.  Races also still have differences based on sex as normal. 

Abilities and Powers:

Due to my inexperience, I was unable to implement a lot of the more unique abilities that I had planned.  I also wanted to have some integration with Ashfall, a mod I love and use religiously, but that's also outside of my limited skillset.  Races now have one ability with a multitude of effects as opposed to several different abilities with one or two effects. Powers are now useful short-term abilities (aside from Bosmer's "Tame Beast"), each race has 1-2 powers, and I have also opted to not have racial spells.

Altmer Ability: Highborn
Weakness to Magicka 50%
Spell Absorption 25%
Resist Common Disease 25%

Altmer Power: Arcane Dominion
Fortify Intelligence 25 pts for 30 Seconds
Fortify Skill: Alteration 15 pts for 30 Seconds
Fortify Skill: Conjuration 15 pts for 30 Seconds
Fortify Skill: Destruction 15 pts for 30 Seconds
Fortify Skill: Illusion 15 pts for 30 Seconds
Fortify Skill: Mysticism 15 pts for 30 Seconds
Fortify Skill: Restoration 15 pts for 30 Seconds

Argonian Ability: Blood of the Hist
Resist Poison 100%
Resist Common Disease 75%
Resist Normal Weapons 10%
Swift Swim 50 points
Water Breathing (will cause issues in the temple quest for obvious reasons, use the console or any other fix you desire to get around this)

Argonian Power: Scalemending
Restore Health 5 pts for 30 Seconds
Restore Fatigue 5 pts for 30 Seconds
Fortify Speed 25 pts for 30 Seconds

Bosmer Ability: Y'ffre's Blessings
Weakness to Normal Weapons 20%
Night Eye 10 pts
Resist Common Disease 50%
Resist Poison 50%
Slow Fall 3 pts 
Jump 5 pts

Bosmer Power 1: Hunter's Sense
Chameleon 15% for 30 Seconds
Fortify Attribute: Agility 25 pts for 30 Seconds
Fortify Skill: Marksman 25 pts for 30 Seconds
Detect Animal 1000 pts for 300 Seconds

Bosmer Power 2: Tame Beast
Command Creature up to Level 15 for 1800 Seconds on Touch
Rally Creature 100 pts for 1800 Seconds on Touch

Breton Ability: Magicka Attunement
Weakness to Normal Weapons 25%
Resist Magicka 50%
Restore Magicka 0-1 pts
Telekinesis 10 pts

Breton Power: Magickynd
Restore Magicka 10 pts for 30 Seconds 
Fortify Willpower 25 pts for 30 Seconds
Shield 25 pts for 30 Seconds

Dunmer Ability: Ashborn
Resist Fire 75% 
Resist Blight Disease 50%
Resist Corprus Disease 25%
Sanctuary 10 pts
Night Eye 10 pts

Dunmer Power: Ancestral Aid
Summon Ancestral Ghost for 30 Seconds
Fire Shield 50 pts for 30 Seconds
Restore Attribute: Strength 1 pt for 30 Seconds
Sound 1 pt for 30 Seconds on Self

Imperial Ability: Empire's Might
Weakness to Blight Disease 25%
Feather 50 pts
Restore Fatigue 0-1 pts
Resist Paralysis 25%

Imperial Power 1: Voice of Colovia
Rally Humanoid 100 pts in 100ft for 30 Seconds on Target
Turn Undead 100 pts in 100ft for 30 Seconds on Target
Demoralize Creature 100 pts in 100ft for 30 Seconds on Target

Imperial Power 2: Voice of Nibenay
Calm Humanoid 100pts in 100ft for 30 Seconds on Target
Calm Creature 100pts in 100ft for 30 Seconds on Target
Charm 100pts in 100ft for 30 Seconds on Target

Khajiit Ability: Feline Physique
Weakness to Fire 10%
Resist Frost 20%
Jump 7 pts
Slowfall 5 pts
Chameleon 5 pts
Night Eye 30 pts

Khajiit Power: Senche's Ferocity
Fortify Skill: Hand to Hand 50 pts for 30 Seconds
Fortify Attribute: Strength 30 pts for 30 Seconds
Sanctuary 25 pts for 30 Seconds
Detect Animal 200 pts for 30 Seconds

Nord Ability: Shor's Endurance
Weakness to Magicka 25%
Resist Frost 75%
Resist Paralysis 50%
Restore Health 0 - 1 pts

Nord Power: Skyborn
Frost Shield 50 pts for 30 Seconds
Feather 100 pts for 30 Seconds
Reflect 15 pts for 30 Seconds
Fortify Speed 25 pts for 30 Seconds


Orsimer Ability: Cursed Might
Drain Attribute: Personality 10pts
Resist Normal Weapons 25%
Resist Magicka 25%
Feather 100pts
Reflect 25%

Orsimer Power: Rage of the Spurned
Fortify Attack 25 pts for 30 Seconds
Fortify Strength 50 pts for 30 Seconds
Resist Paralysis 50 pts for 30 Seconds
Blind 50 pts for 30 Seconds on Self
Drain Attribute: Agility 50 pts for 30 Seconds on Self

Redguard Ability: Ra Gada Toughness
Weakness to Frost 20%
Resist Common Disease 50%
Resist Paralysis 50%
Resist Fire 10%
Restore Attribute: Strength 0 - 1 pts

Redguard Power: Sand of the Alik'r
Chameleon 15 pts for 30 Seconds on Self
Fortify Attack 50 pts for 30 Seconds on Self
Fortify Attribute: Agility 25 pts for 30 Seconds on Self
Restore Fatigue 5 pts for 30 Seconds on Self
Sanctuary 20 pts for 30 Seconds on Self