Man, I sat through all 6 of those OVAs hoping for a proper conclusion, and I'm still a bit miffed. The anime, 'Broken Blade', condenses the first part of the manga into those six hour-long episodes, but it just... stops. It ends right after the big duel with Borcuse at the White Forest, which is maybe around volume 4 or 5 of the manga?
In the manga, that's nowhere near the end. The story keeps going for way more volumes, delving deeper into the politics of the continent, the true nature of the Golems, and Rygart's own mysterious past. Characters like Sigyn and Cleo get way more development, and there are entire arcs about other kingdoms that the anime never touches.
So the difference isn't really a 'different ending'—it's more like the anime hits the pause button on a much larger story. It's a solid adaptation of the early action, but you're left hanging on every major plot thread. I had to hunt down the scans to get any closure, and even then, I'm not sure the manga itself is fully finished in English.
You watch the anime for the fantastic, crunchy mecha battles, but you read the manga to actually understand what's going on.