I don't believe the Romans actually had steel at all. Their weapons were iron. However its possible some carbon migrated into the surface and edges of the iron blades giving it a harder surface. But such weapons are not true steel and will not have the same strength.
Can you provide some source for the Migration Era Roman sword? I suspect it's not Roman but rather a "barbarian" sword which used a typical forge folded method of welding iron and steel together.
That method was fairly common after the 3rd century, though it was not always used for technical reasons (it appears that a lot of Germanic smithsconsidered it decorative). On Roman steels (and they did not produce steel in the smelting process but by forging techniques), a good introduction is Junkelmann, M.: Die Reiter Roms, Vol III, pp. 130 ff. The usual process was most likely 'case hardening' (raising carbon content by long exposure to carbon at about 900°C) preceded by exposure to nitrogen.
The typical imperial Ropman sword blade was made as a combination of iron and steel, with steel (a very expensive material) used only sparingly, either deliberately created on the surface (which rarely survives in the archeological record) or used separately to make the edges and stiffening the core. A Mainz-type sword from Cologne was made by adding steel edges and sides to an iron core and records 670 HV along the edge and 500 HV in the core. The other two early blades studied came in between 770 HV and 500 HV along the edges (not homogenous). Four later (1-2 century AD) blades from the Rhineland also spread between 600 HV and 740 HV along the edges.
Other blades from broadly the same timefrane use less hardened steel, especially the Pompeii-type sword whose blade shape may have been designed to allow the uise of softer material in the first place. An example from Vindonissa uses an iron core (c. 100 HV) with mild steel edges and covering (up to only 216 HV), while a spatha from Whittlesey came in at between 159 HV and 193 HV. Here, carbon content was measured and found to be between 0.2% and 0.3%
Many late antique and early medieval pattern-welded blades are actually of lower hardness than Principate-era Roman weapons, though the method may have created a more flexible, less brittle weapon more reliably (the Roman sandwiching process is very difficult). They also used less coal in the manufacture. The finds from Southern Germany are unusual in this regard and appear to have been sourced from the Roman Mediterranean.
If the Romans had advanced steel making technology they would be able to mass produce iron and steel which would be a major gain for military and agriculture (swords and plowshares). This means larger armies and more food and thus could be transformative.
Only if they had been able to produce steel in large quantities cheaply (and the quality is less important there - even unhardened iron would make a huge difference if it was available at a fraction of the price).