my answer is extension to circulant and recursive.
one property measure to the optimal implementation of MDS matrix in cryptography is the cost of xor (number of xors required to fully implement the MDS matrix ) , depth (number of stages) and the field size (usually 4 or 8 )
according to this paper MDS Matrices with Lightweight Circuits, the native implementation of AES MDS matrix costs 152 xors , with the improved algorithm is reduced to 97 xors and depth of three stages.
they searched for others MDS with different structures such as Toeplitz and Hadamard.
Figures below show better MDS matrices in term of implementation compared to circulant AES MDS .
In addition to hardware cost, the security aspect of MDS matrix has appeared in this paper : MixColumns Properties and Attacks on (round-reduced) AES with a Single Secret S-Box, which takes advantage of MDS values.
At the end , it is your call which MDS matrix to be implemented , you need to look it from security and hardware implementation cost.