With an Invulnerability Tanker, you're at the Hit point cap with Dull Pain up, so I'd advise the +Regen version instead of the +hit point version. So go Radial Rebirth.
You can have both. Get both.
But Radial Rebirth is very good as a second heal and helps to 'stabilize' your HP bar.
Barrier is good for shrugging off an alpha strike (especially one like the Clockwork King in the LGTF) and keeping you upright during an Unstoppable crash, if you use that power.
Both are situational.
Again, you can have both, get both.
And get Ageless for when you want to pump a bit more damage. It'll also help your Dull Pain get back up faster.
.
Sounds like Radial Rebirth is it then. 
Now to run a few more trials 
Combat Kangaroos, Justice Server. First 50's
Jirra Roo Plant/Storm/Stone/Musculature Controller
Combat Kangaroo Rifle/Energy/Mace/Spiritual Blaster
Kung Fu Kangaroo Martial Arts/Reflexes/Body/Spiritual Scrapper
Tribal Arc Shield/Elec/Mu/Spiritual Tanker
Radial Rebirth is my default choice on nearly all characters; a massive heal coupled with a perma (at tier 3) +200% regen with much more over half of the duration. Baring a character with specific needs that another Destiny fills this is what I go with.
On the other hand unless it's changed in the last issue the Core Rebirth is a pile of crap; it's a fixed, relatively low amount of +HP and doesn't vary by AT. It's... odd to see such a massive discrepancy in the functionality of a Core and Radial tree. I really wish there were some valid reason to choose Core but as it stands Radial is so much better it isn't even in the same ballpark.
COH has just been murdered by NCSoft. http://www.change.org/petitions/ncso...city-of-heroes
For my Inv characters, the choice between Rebirth or Barrier was easy, and the answer was Ageless.
Here is my current build on my Inv/SS tanker on Justice. It is softcapped to all but psi with 1 mob in range. I also have a tweak to it where I drop a slot from combat jumping, put that slot in TI and use the Gladiators +3% defense, puts me at nearly 50% defense, not bad on top of my resists a +hp heal and unstoppable. Also, I am swapping out the Cardiac for an Agility, I still want the endurance, but I can easily handle the extra recharge... and recharge is always good.
My question is, Rebirth or Barrier? Im leaning towards rebirth, not sure which one I want yet though as i've yet to use Rebirth on any character yet. Or is there another one I should consider?
Hero Plan by Mids' Hero Designer 1.952
http://www.cohplanner.com/
Click this DataLink to open the build!
The Boxing Kangaroo: Level 50 Magic Tanker
Primary Power Set: Invulnerability
Secondary Power Set: Super Strength
Power Pool: Leaping
Power Pool: Fighting
Ancillary Pool: Energy Mastery
Hero Profile:
Level 1: Temp Invulnerability -- RctvArm-ResDam(A), RctvArm-ResDam/EndRdx(3), RctvArm-ResDam/EndRdx/Rchg(3), RctvArm-EndRdx(5)
Level 1: Jab -- KntkC'bat-Acc/Dmg(A), KntkC'bat-Dmg/EndRdx(5), KntkC'bat-Dmg/Rchg(7), KntkC'bat-Dmg/EndRdx/Rchg(7)
Level 2: Dull Pain -- Dct'dW-Heal/EndRdx(A), Dct'dW-EndRdx/Rchg(11), Dct'dW-Heal/Rchg(13), Dct'dW-Heal/EndRdx/Rchg(13), Dct'dW-Heal(15), Dct'dW-Rchg(48)
Level 4: Haymaker -- KntkC'bat-Acc/Dmg(A), KntkC'bat-Dmg/EndRdx(15), KntkC'bat-Dmg/Rchg(17), KntkC'bat-Dmg/EndRdx/Rchg(17)
Level 6: Resist Elements -- Aegis-ResDam(A), Aegis-ResDam/EndRdx(19), Aegis-ResDam/Rchg(19)
Level 8: Unyielding -- RctvArm-ResDam(A), RctvArm-ResDam/EndRdx(9), RctvArm-ResDam/EndRdx/Rchg(9), RctvArm-EndRdx(11)
Level 10: Combat Jumping -- LkGmblr-Rchg+(A), LkGmblr-Def(34)
Level 12: Resist Energies -- Aegis-ResDam(A), Aegis-ResDam/EndRdx(33), Aegis-ResDam/Rchg(33)
Level 14: Super Jump -- Jump-I(A)
Level 16: Resist Physical Damage -- S'fstPrt-ResDam/Def+(A), Aegis-ResDam/EndRdx(46), Aegis-ResDam(46), Aegis-ResDam/Rchg(48)
Level 18: Invincibility -- LkGmblr-Rchg+(A), LkGmblr-Def(34), LkGmblr-Def/EndRdx(34), LkGmblr-Def/EndRdx/Rchg(37)
Level 20: Knockout Blow -- Mako-Acc/Dmg(A), Mako-Dmg/EndRdx(21), Mako-Dmg/Rchg(21), Mako-Acc/EndRdx/Rchg(23), Mako-Acc/Dmg/EndRdx/Rchg(23), Mako-Dam%(29)
Level 22: Kick -- Acc-I(A)
Level 24: Tough -- RctvArm-ResDam(A), RctvArm-ResDam/EndRdx(25), RctvArm-ResDam/EndRdx/Rchg(25), RctvArm-EndRdx(27)
Level 26: Tough Hide -- LkGmblr-Rchg+(A), LkGmblr-Def(27), LkGmblr-Def/EndRdx(33)
Level 28: Rage -- GSFC-ToHit(A), GSFC-ToHit/Rchg(29), GSFC-ToHit/Rchg/EndRdx(43), GSFC-Rchg/EndRdx(45), GSFC-ToHit/EndRdx(45), GSFC-Build%(46)
Level 30: Weave -- LkGmblr-Rchg+(A), LkGmblr-Def(31), LkGmblr-Def/EndRdx(31), LkGmblr-Def/EndRdx/Rchg(31)
Level 32: Unstoppable -- RechRdx-I(A)
Level 35: Taunt -- Mocking-Taunt(A), Mocking-Taunt/Rchg(36), Mocking-Taunt/Rchg/Rng(36), Mocking-Acc/Rchg(36), Mocking-Taunt/Rng(37), Mocking-Rchg(37)
Level 38: Foot Stomp -- Erad-Dmg(A), Erad-Acc/Rchg(39), Erad-Dmg/Rchg(39), Erad-Acc/Dmg/Rchg(39), Erad-Acc/Dmg/EndRdx/Rchg(40), Erad-%Dam(40)
Level 41: Hurl -- Thundr-Acc/Dmg/EndRdx(A), Thundr-Acc/Dmg/Rchg(42), Thundr-Dmg/EndRdx/Rchg(42)
Level 44: Conserve Power -- RechRdx-I(A), RechRdx-I(45)
Level 47: Physical Perfection -- Efficacy-EndMod(A), Efficacy-EndMod/Rchg(48)
Level 49: Laser Beam Eyes -- Thundr-Acc/Dmg/EndRdx(A), Thundr-Dmg/EndRdx/Rchg(50), Thundr-Acc/Dmg(50), Thundr-Acc/Dmg/Rchg(50)
Level 50: Cardiac Core Paragon
------------
Level 1: Brawl -- Acc-I(A)
Level 1: Gauntlet
Level 1: Sprint -- Run-I(A)
Level 2: Rest -- RechRdx-I(A)
Level 4: Ninja Run
Level 2: Swift -- Run-I(A)
Level 2: Health -- Numna-Regen/Rcvry+(A), Numna-Heal(43), Numna-Heal/EndRdx(43)
Level 2: Hurdle -- Jump-I(A)
Level 2: Stamina -- P'Shift-EndMod(A), P'Shift-EndMod/Rchg(40), P'Shift-EndMod/Acc(42)
Combat Kangaroos, Justice Server. First 50's
Jirra Roo Plant/Storm/Stone/Musculature Controller
Combat Kangaroo Rifle/Energy/Mace/Spiritual Blaster
Kung Fu Kangaroo Martial Arts/Reflexes/Body/Spiritual Scrapper
Tribal Arc Shield/Elec/Mu/Spiritual Tanker