First of all, I'm assuming when you refer to accuracy you used cross validation to asses how good the model predicts the classification outcome. Even if your training sample size goes to infinity, it might be that your model is not able to correctly predict outcomes based on the features.
In the case of SVMs, remember a hyperplane is constructed that minimizes misclassifications (of the training set) and maximizes the decision boundary. For a 2d visual representation see: http://www.saedsayad.com/support_vector_machine.htm
As more datapoints are added, we would expect our classifier to increase its performance up to a certain point. This depends on how well our model is capturing the variability present in the data. To quote George Box: "All models are wrong, but some are useful". You could imagine that if you have an infinite amount of samples but the features in the samples are not adequate to explain all the variation in the sample, we would still have misclassifications. In my opinion, this is probably what is happening in your example. The iris dataset probably contains features that explain the variability quite well and this ensure a good decision boundary (in SVM). The wine dataset might contain many samples that even after optimization of the decision boundary contain a lot of misclassifications. The comparison between your two datasets isn't fair because they can differ in their features. A better approach would be to take a huge dataset and first start with a small part of it to train a classifier. Gradually increase sample size and performance will most likely increase.
From my limited understanding of Neural Networks, I'm not sure your samplesizes mentioned here are adequate for such an algorithm. There are rules of thumb, depending on the number of layers etc. As you didn't mention what algorithm or setup was used for the Iris or Wine dataset, a quick reference can be found here: ftp://ftp.sas.com/pub/neural/FAQ3.html#A_hu
Now onto your question. If by descriptive you mean how well the sample (that is your dataset) represents the total population from which it is drawn, you need more samples to check this. If you meant how descriptive my dataset is (in this case, how well does it classify) without actually training the algorithm and testing it, that would be really difficult exept for very simple datasets. If we go back to the two dimensional SVM example I linked, a simple scatterplot with labels for the two classes gives you a good idea how well a binary linear classifier would preform. As soon as we enter a higher dimensional feature space or have many possible outcomes, things get difficult. The above mentioned is just a visual inspection of the data, I can't think of any quantifiable way. But this leads me to the question, why would you want this in the first place?
I hope I've been some help to you, feel free to ask more if something isn't clear.