I've actually done variants of that experiment - and I've always concluded that the augmented adept pulls further and further ahead of the pure adept. If you disagree, I think it's most likely because you are building the augmented adept in an inefficient way. I think the strongest argument would be this: make me a pure, no augmentations adept on 400BP, then add 200 karma and 500,000 nuyen. After I see what you are focused on, I'll make an equivalent augmented character that is numerically more efficient.
Before I drop here a fast combat build of an adept, I have to say, that I am kinda suprised, that nobody here mentions Adept centering. This ability is not to be underestimated, because you have negative modifiers in every fight, and if they really are not present, you can make your own (called shots to avoid armor, called shots to increase DV, shooting from cover/+ moving vehicle etc.)
400BP Human adept
Qualities: (+10)
-5 Adept
-10 Warriors way ( Improved reflexes, Combat sense, Mystic armor, @magic 8 - Improved Ability ) ; preffered X Gease optional rule)
-10 Perceptive
+5 Prejudiced (Gypsies)
+10 Amnesia
+10 Records on file
+10 Vindictive
Attributes: (-305)
-30 Body (4)
-40 Agility (5)
-20 Strength (3)
-40 Reaction (5)
-0 Charisma (1)
-40 Intuition (5)
-10 Logic (2)
-20 Willpower (3)
-40 Edge (6)
-65 Magic (6)
0 Essence (6)
Skills: (-98)
-26 Pistols ( or Automatics,... etc.) (6/8)
-18 Perception (4/6)
-18 Assensing (4/6)
-18 Unarmed (4/6)
-6 Dodge (1/3)
-6 Infiltration (1/3)
-6 Survival (1/3)
Powers: (PP - 6)
-3 Improved reflexes III
-0,75 Combat sense II
-0,75 Mystic armor II
-1 Astral Perception
-0,5 Enhanced Perception II
Equipment is not so important at this point, cause even if you spent a lot of nuyen for augmentaion, we still can +- buy the same things.
Advancement: (200 karma)
-76 Initiation grade (1-6) (Adds 5 power points + Adept centering - 7 dice now)
PPoints to spend: (5)
-1,5 Combat sense II -> VI
-0,75 Mystic armor II -> IV
-1,5 (-1,125) Improved Ability III (Pistols)
-0,5 Quick draw
-0,25 Attribute boost I (Agility)
-0,5 Enhanced Perception II -> IV
-75 Magic (7,8)
-40 Init. grade (7,8) (Adds 2 power points + Attunement item - any pistol + Masking metamagic)
PPoints to spend (2,375)
-0,75 Combat sense VI -> VIII
-1,5 Mystic armor IV -> VIII
-8 Attunement item bond
So in this teoretical exaggerated example, you have Adept centering @ 9 dice (which is rather insane), Attunement item bonus @ 5 dice, +8 Armor, +8 on reaction defensive and anti-suprise rolls, perception rolls with 16/18 dice, same goes for Assensing rolls. Attack rolls with pistol are at 21 dice, modified by any success from Attribute boost power( 9 dice so +-3 likely). Ranged defense @ 16 dice, melee @ 19 dice.
There are also other variants you can use. Using the Gease optional rule will add even more power points, rolling an elf for aditional agility, or adding Changeling II quality for metagenetic improvement ( intuition or agility), but these changes dont influence the ware/no ware difference (=.
An unarmed melee variant would also be interesting to compare. Because I think a possible muscle toner/augmentation, synaptic booster and other bioware upgrades that can fit in a -2 essence loss, cant profit over the 4 point of power points and 2 initiation grades loss.
Last thing I want to mention, as I saw your gunslinger character, in the advancement section, you cant increase your magic 3(5) - reduced by 2 with bioware - by 20 karma points to get a magic 4, you need to spend 30 karma as if your magic was 5 and you wanted to increase it to 6, then applying the -2 from essence loss. Hope it helps.