+ Comparison of the two solutions

We start by looking at the acceleration curves which give us a feel for the force on the follower. The second solution has a larger maximum absolute value.

Input := 

Show[p1a,p2a]
Output =

-Graphics-

but the jerk of the polynomial solution (first solution) has a somewhat larger value. It's a hard call.

Input := 

Show[p1j,p2j]
Output =

-Graphics-