Stability of isomers of N4O
From The Nitrosyl Azide Potential Energy Hypersurface: A
High-Energy-Density Boom or Bust? J. Am. Chem. Soc. 1996, 118, 4860-4870 :


  [Abstract] ...While the ring isomer is predicted to be the most stable structure on the
  hypersurface, the barrier to dissociation is most likely between 1 and 2 kcal mol-1 (including zero-point vibrational
  energy [ZPVE], the existence of any barrier becomes questionable) making isolation theoretically possible but
  experimentally difficult. This small barrier also detracts from the attractiveness of the N4O ring structure as a high energy-density material. The trans-chain isomer, however, lies in an energy valley with higher sides, consistent
  with its previous experimental observation.
  
  [full text]...In an ideal five-membered ring
  with 6 $\pi$ electrons, the $\pi$ electrons would be distributed evenly
  among all the bonds. In the present case, the highly electronegative
  O atom prefers to keep electrons around itself, leading
  to a partial negative charge on the oxygen. Energetically, there
  is a certain degree of stability associated with the ring isomer,
  although not on the order of common aromatic systems. The
  ring isomer is predicted to be at most (DZP CISD) 20.9 kcal
  mol-1 more stable than the trans-chain isomer; however, this
  value decreases to 13.2 kcal mol-1 with TZ2P CCSD.
  The ring isomer TS to dissociation into N2 and N2O is shown
  in Figure 5. ... Energetically, the barrier to dissociation
  is at most 15.3 kcal mol-1 (DZP CISD) and drops lower
  with improvements in both basis set and correlation scheme.
  In going from a DZP to a TZ2P basis set, for example, this
  barrier drops by 5.2 kcal mol-1 for CISD and 4.3 kcal mol-1
  for CCSD. Assuming a similar trend in moving from DZP
  CCSD(T) to TZ2P CCSD(T), the ring dissociation barrier is
  expected to drop to 1-2 kcal mol-1 with the addition of f-type
  functions possibly making it even lower. A barrier of this size
  lies below the ZPVE, throwing doubt on the existence of the
  N4O ring isomer.


So thermodynamically, yes, the ring form is the lowest energy isomer.  However, all the isomers are unstable to decomposition and the linear isomer is in a deeper potential energy well than the ring isomer. Therefore, the linear isomer is easier to observe experimentally for kinetic reasons.  

There may be additional information in Theoretical study on structures and stabilities of N4X (X = O, S, Se, Te) series International Journal of Quantum Chemistry Volume 109, pages 226–235.