If you do not have a lot of data, then univariate series could be the only way to go. For instance, in the simplest 2D VAR(1) you have the following:
where $X$ - two dimensional vector of observable series, $\Phi_1$ - 2x2 matrix of lags, and $\Sigma$ - 2x2 matrix of error covariances. So, you have 2 intercepts, 4 lag coefficients, 2 variances and one covariance to estimate, i.e. 9 parameters in total.
If this was two univariate models you'd have: one intercept, one autocorrelation coefficient and one variance. This makes it 6 parameters in total, i.e. 3 fewer parameters to estimate. In general the number of parameters is linear to the number of dependent variables, while in VAR it's quadratic growth. If you have multiple lags and many dependent variables the number of parameters quickly gets out of control.
When you increase number of parameters the system becomes unstable, very sensitive to small variations in the sample, unless your sample is very large.