Soulborn 20:
5 Soulmelds (ML 10 for all)
13 Essentia from class levels
3 Chakra binds
Incarnate 2/Fighter 18:
3 Soulmelds (ML 2 for all)
2 Essentia from class levels
1 Chakra Bind
I2/F18 with 2 Shape Soulmeld feats, 2 Open Chakra Feats, Bonus Essentia and 3 incarnum feats:
5 Soulmelds (ML 2 for 3, 10 for 2)
7 Essentia
3 Chakra Binds
Fighter 20 at its best:
5 Soulmelds (ML 10)
0 Essentia
2 Chakra Binds
{Soulmelds/Binds/Essentia can be arranged at a 1:1 rate, depending on what you're going for, but the count is lower than Soulborn regardless of the array}
The Fighter builds would still have 10-11 fighter feats to build up some combat shtick, compared to the Soulborn's 7 free feats (11-12:8 if Azurin), but even the Incarnate/SoulbornFighter would still fall 6 essentia short.
Unless you consider the Dark Chaos shuffle practical op, I'm having a hard time seeing the Fighter coming out ahead.