No. The LMG34 is not more useful.
The IR STG44s actually have more DPS than the LMG34 at max range as long as the enemy unit is in cover, because of their 0.9 cover accuracy multiplier.
The rare chance of grabbing a second LMG or if the enemy never uses cover are the only two scenarios in which the LMG34 upgrade is better.
Dps on heavy cover enemy for LMG34 at max range: 14.22 x 0.5 = 7.11
Dps on heavy cover enemy for IR stg at max range: 3.183 x 0.9 = 2,86
From 23 range up to 35 range even with the cover bonus an IR STG deals less dps to the enemy