While we await the final set of assumptions that go into the this comparison it might be interesting to talk about expected results.
I expect the fighter to be ahead in tier 1 by a little bit. At this stage, wizards run out of spells quickly if you have a long adventuring day and without ability bumps to cantrips in most cases, casters can't keep up via cantrips along.
Tier 2 when large AoE spells come online, cantrip damage increases to keep pace with Extra Attack (mostly), and more spell slots become available, I expect the wizard to begin edging out the fighter in some cases. A lot depends on scenario set up, how much GWM and other feats might make an impact, and so forth.
Tier 3 the wizard has enough spells to beat out the fighter in many (not all) scenarios. By this point they also have spells and a good enough save DC that can turn the tide of an encounter, allowing them to utilize for damage better.
Tier 4 there is no contest IMO. Wizard wins out with so many spells and options. With Extra Attack (3) not coming online until level 20 (it should be level 17 IMO), the fighter suffers. With Action Surge their burst damage can be great given a more optimized build, but they just can't maintain it. The fact a wizard will typically only get 1 spell per turn at this point helps them by preserving their spells and keeping them from truly novaing.
Summary: Fighters should be supreme when it comes to combat IMO, but after tier 1 they have moments but struggle to keep pace over all. For me, the answer isn't to make fighters better, but to give them some options to contribute outside of combat as every other class can (for the most part) and rein in casters a bit (and others) to not be
as effective in combat.
That's my prediction, anyway.
My post above about Jedi really got me thinking. The jedi are more powerful in many ways certainly, but IME d20 SW kept things balanced enough that non-jedi never really felt outclassed completely. Two things helped in this respect I think. 1) Jedi has much more limited force abilities (both in scope of utility and power) and 2) Jedi had to spend hit points (i.e.
vitality) to empower their force use.
If D&D casters had to spend hit points instead of having spell slots... they might not be as eager to cast (provided the idea was adopted correctly, a "direct transfer" doesn't work).