The lesser powered version - the one that fought Thanos - would win too, and pretty handily I would think. The thing that saved Thanos was 1. The Orb and 2. His durability.
Darkseid is less durable, and doesn't have the orb. While I think his Wipe Out beams and Omegas in general would definitely help out and would hurt Tyrant, the outcome would never really be in doubt.
Maybe Tyrant has taken down Beta Ray Bill ,Silver Surfer ,Gladiator and some other guys but Kirby's Darkseid feats way beyond that.The Omega Effect would possibly work on him (Imo) since he is not important for the Source neither more powerful then DS (some guys like to say that the Omega Effect only works on those who are less powerful then Ds)
Also he has defeated and stalemated High Father who is atleast "skyfather" level and he was feared by Panthenons even his father Yuga Kahn was afraid of him.Darkseid was able to beat the Pre-Crisis JLa in 1 panel also he beat Pre-Crisi Superman numerous times who was able to destroy a solar system only with a sneeze.
He was able to damage a wounded AntiMonitor (some guys here consider it as PIS) and he was also able to hurt (Hal Jordan) Spectre with the OB.
some feats:
Depowered Tyrant's biggest feat is smacking around Surfer ,BRB ,Gladiator and the others while Darkseid has beaten Pre-crisis JLA in 1 panel.
Decide which is the better feat...
That is not depowered Tyrant. As I sad before that happened during the fight with Galactus. Where did you get that he dstroyed hundreds of galaxies cause the comic never mentioned that.