How will node handle two branches of same length? Let's say node is on a chain of length N+4, and receives a block from the chain of the same length N+4, but diverged by 4 blocks.


Is the information of the length and accumulated difficulty broadcasted along with mined block?
How will the recipient node handle this situation?
This phenomenon is known as a chain-split (i.e. the bitcoin network can no longer agree which chain is the canonical chain).

Nodes will be network-partitioned until one chain becomes dominant.

Therefore:


  Is the information of the length and accumulated difficulty broadcasted along with mined block?


No. 


  How will the recipient node handle this situation?


Nodes will handle equal branches on a First Come, First Serve basis, so there will be a network partition where some nodes agree chain A with length N+4 is the canonical chain and the other set of nodes will assume chain B with length N+4 is the canonical chain. In the event of such a chain-split, the race is on for miners to produce a new block-tip and broadcast it across the bitcoin network ASAP to achieve convergence. When the contention is resolved, the node can switch to longer branch and obsolete the old branch.