ParticleSystem dynamic batching doesn't work

The section from Draw Call Batching manual page specifies the criteria for dynamic batching as:

Batching dynamic objects has certain overhead per vertex, so batching is applied only to meshes containing less than 900 vertex attributes in total. - If your shader is using Vertex Position, Normal and single UV, then you can batch up to 300 verts; whereas if your shader is using Vertex Position, Normal, UV0, UV1 and Tangent, then only 180 verts.

Which is an important part since when your render mode is billboard the number of vertices must be satisfying the vertices count for this but when you choose a mesh the vertices count is exceeding these limits and hence you are not being benefited with dynamic batching. You can just check this by looking at the Vertices count from Stat when you switch between billboard and mesh render mode.