You are looking at a vast swath of time. Legions of the early to middle Republic were very uneven since they were just militias mobilized for specific campaigns. Now the frequent nature of campaigning meant that a significant percentage of the men had been in battles and were veterans - however each legion was a new force that needed to build up its internal cohesion. It doesn't matter if every man in a legion is a 10yr veteran if none have served physically alongside each other and implicitly trust each other when the arrows start flying.

This meant that these Republican legions could be very fragile when mobilized. Many disasters happened when an impatient consul marched his newly mustered legions right off towards his province. Those who took some time to drill the army and allow for some unit cohesion to develop would have a more solid and reliable force.

But the thing to remember is that all of these are temporary formations raised to fight in a single campaign. There was no unit history since each legion was raised from scratch and assigned a designation of 1 - 4 (two being commanded by each consul). Obviously as Rome's commitments increased then more legions would have to be raised but these were still temporary formations that would be disbanded upon completion of their task. Campaigns in the early Republic were against local enemies so the fighting was usually over in a year. By the middle Republic, Rome was controlling or fighting in foreign territories which meant you had to factor in travel time for the army to march to the province. Some provinces proved to be rather intractable or possessed an enemy who wouldn't meet the Romans in a winner-take-all pitched battle and so these campaigns would drag on for years (i.e. Spain). Those unlucky armies would have good cohesion having worked together for years now but would likely have morale issues because they'd been on campaign for years.

I'm bypassing the late Republic because that's when the wheels fell off and I can't describe it in sufficient detail.

The Principate under Augustus is when you see the professionalization of the legions with a fixed term (20 years, later changed to 25) and a defined payout at the end. At this point legions were individual institutions with a unit character and nickname (e.g. Legio V Macedonia pia fidelis).

I would also note that Carrhae and Hannibal are separated by a century and a half - very different legions were involved.