Using the "smoothing" technique involves downplaying conflicts or differences and emphasizing commonalities to maintain peace and harmony. While this can provide a temporary solution, it often doesn't address the root cause of the conflict. In the scenario you provided, where two team members have significant professional differences that have impacted their performance, merely emphasizing areas of agreement without addressing the root cause may not be effective in the long term. The conflict could resurface later if not genuinely resolved.
On the other hand, "negotiating" involves actively addressing the conflict and trying to find a mutually acceptable resolution. By mediating a negotiation between the two team members, the project manager can help them address their differences and reach an understanding. This approach can lead to a more lasting resolution, allowing the team to move forward productively.