The two sects in Sri Vaishnava sampradayam arose during the time of Sri Pillai Lokacharyar and Swami Vedantacharya (Vedanta Desikan). Both are great acharyas in our Sampradayam. There are around 18 differences between two sections.
The differences mainly come regarding the role of Mahalakshmi, our effort to reach Narayana etc.
In any society to survive happily with so many sections, one thing should be remembered by all the sections.
"Worship Your Own and Respect All"
I may not be sure these two will unite one day but I am sure we can live happily together if we follow the above rule.