Understanding Classifier performance on text data
As the data is imbalanced and skewed towards few classes, that's why RF and Logistic results are biased causing high FP values, therefore high precision and low recall.
SVC on the other hand might have tried to create hyperplanes to get most out of the other side of curve, thereby producing different results.

To improve the results, try to use non linear kernels and also try to balance the input data (by scaling etc) before feeding to classifiers.