That being said, I did the first 6 levels of a Fighter 1/Warlock X vs a Eldritch Blade X anyway, because it's useful information.
Assuming both went for Fiendish Vigor as an invocation, and that both took the Duelling fighting style:
Fighter 1 | Eldritch Blade 1
High dmg: 1d8+5 High dmg: 1d8+5
Low dmg: 1d8+5 Low dmg: 1d8+5
Avg dmg: 9.5 Avg dmg: 1d8+5
Effective Avg HP: 32.5 Effective Avg HP: 13
AC: 17 AC: 17
Fighter 1/Warlock 1 | Eldritch Blade 2
High dmg: 1d8+1d6+5 High dmg: 1d8+1d6+5
Low dmg: 1d8+5 Low dmg: 1d8+5
Avg dmg: 11.25 Avg dmg: 11.25
Effective Avg HP: 40.5 Effective Avg HP: 54
AC: 17 AC: 17
Fighter 1/Warlock 2 | Eldritch Blade 3
High dmg: 1d8+1d6+5 High dmg: 1d8+1d6+5
Low dmg: 1d8+1d6+5 Low dmg: 1d8+1d6+5
Avg dmg: 13 Avg dmg: 13
Effective Avg HP: 80.5 Effective Avg HP: 63
AC: 17 AC: 17
*Not included Martial Archetype
Fighter 1/Warlock 3 | Eldritch Blade 4
High dmg: 1d8+1d6+5 High dmg: 1d8+1d6+6
Low dmg: 1d8+1d6+5 Low dmg: 1d8+1d6+6
avg dmg: 13 Avg dmg: 14
Effective Avg HP: 88.5 Effective Avg HP: 72
AC: 17 AC: 18
Fighter 1/Warlock 4 | Eldritch Blade 5
High dmg: 1d8+1d6+6 High dmg: 2d8+2d6+6
Low dmg: 1d8+1d6+6 Low dmg: 2d8+2d6+6
Avg dmg: 14 Avg dmg: 28
Effective Avg HP: 86.5 Effective Avg HP: 81
AC: 18 AC: 18
Fighter 1/Warlock 5 | Eldritch Blade 6
High dmg: 2d8+2d6+6 High dmg: 2d8+2d6+6
Low dmg: 2d8+2d6+6 Low dmg: 2d8+2d6+6
Avg dmg: 28 Avg dmg: 28
Effective Avg HP: 94.5 Effective Avg HP: 90
AC: 18 AC: 18
As you may be able to discern, the Fighter 1/Warlock X has more effective HP, for the price of delaying a boost to attacking. Level 6 is actually wrong, as the Fighter/Warlock gets 3rd level spells, and thus Hex lasts longer than 1 combat. As both classes progress, the Eldritch Blade should take over in effective HP and melee damage output, while the Fighter/Warlock will gain more high level spells and quicker.