The reason is generally that while ELISA gives you a readout for the amount of virus specific antibody (it's a quantitative test) a virus neutralization test gives you a readout for the amount - and quality - of antibody produced that can neutralize the virus (it's a qualitative test) and thus (potentially) actually protect an organism from infection. There have been cases where a vaccine candidate induces a great antibody response (as in quantity of antibody produced able to bind the virus) giving a high ELISA score but an (almost) non existent neutralizing response.

You could see: Meng, J., P. Dubreuil, and J. Pillot. "A new PCR-based seroneutralization assay in cell culture for diagnosis of hepatitis E." Journal of clinical microbiology 35.6 (1997): 1373-1377.

Stanfield BA, Stahl J, Chouljenko VN, Subramanian R, Charles A-S, et al. (2014) A Single Intramuscular Vaccination of Mice with the HSV-1 VC2 Virus with Mutations in the Glycoprotein K and the Membrane Protein UL20 Confers Full Protection against Lethal Intravaginal Challenge with Virulent HSV-1 and HSV-2 Strains. PLoS ONE 9(10): e109890. doi:10.1371/journal.pone.0109890

The described method worked well for me but I did not achieve complete neutralization. Using a lower concentration of virus (~100 pfu) will help get your numbers closer to 0.

You could also use the pseudotype virus neutralisation assay, depending on the virus you study.

Pseudotypes are replication-deficient, chimeric viral particles that mimic wild-type virus entry mechanisms, and permit serology and neutralising antibody quantification of pathogenic viruses without the need for high containment laboratories. They are safe, cheap and highly flexible with regards to the reporter gene encapsulated into/envelope glycoprotein coating the (often retroviral) core. They also display comparable sensitivity and specificity with more traditional serological assays that utilise wild-type virus. 

See:

Temperton, N.J., Wright, E., 2009. Retroviral pseudotypes. In: Encyclopedia of Life Sciences. John Wiley & Sons, Chichester.

Temperton, N.J., Hoschler, K., Major, D., Nicolson, C., Manvell, R., Hien, V.M., Ha, D.Q.,de Jong, M., Zambon, M., Takeuchi, Y., Weiss, R.A., 2007. A sensitive retroviral pseudotype assay for influenza H5N1-neutralizing antibodies. Influenza Other Respir. Viruses 1, 105–112.

Wright, E., Temperton, N.J., Marston, D.A., McElhinney, L.M., Fooks, A.R., Weiss, R.A.,2008. Investigating antibody neutralization of lyssaviruses using lentiviral pseudotypes: a cross-species comparison. J. Gen. Virol. 89, 2204–2213.

Temperton NJ, Chan PK, Simmons G et al. Longitudinally profiling neutralizing antibody response to SARS coronavirus with pseudotypes. Emerg. Infect. Dis. 11(3), 411–416 (2005).

Mather, S., Scott, S., Temperton, N., Wright, E., King, B., Daly, J., 2013. Current progress with serological assays for exotic emerging/re-emerging viruses. Future Virol. 8, 745–755.

Ferrara F, Molesti E, Bottcher-Friebertshauser E et al. The human transmembrane protease serine 2 is necessary for the production of group 2 influenza A virus pseudotypes. J. Mol. Gen. Med. 7, 309–314 (2012).

Hope this helps!

The reason is generally that while ELISA gives you a readout for the amount of virus specific antibody (it's a quantitative test) a virus neutralization test gives you a readout for the amount - and quality - of antibody produced that can neutralize the virus (it's a qualitative test) and thus (potentially) actually protect an organism from infection. There have been cases where a vaccine candidate induces a great antibody response (as in quantity of antibody produced able to bind the virus) giving a high ELISA score but an (almost) non existent neutralizing response.

Mundkur LA, Shivanandan H, Hebbagudi S, Endrész V, Varma M, Rao V, Gonczol E,

Kakkar VV. Human cytomegalovirus neutralising antibodies and increased risk of

coronary artery disease in Indian population. Heart. 2012 Jul;98(13):982-7.

I agree with Hans-Peter, I'm using both VNT and ELISA to test canine distemper virus vaccines, I thinh they give complementary results ;)