I have a dataset of what apps users downloaded and I try to estimate these users' gender based on what apps they downloaded, using machine learning algorithm. However, what kind of features of the apps should I focus on? As far as I know, app category plays a big role. Do Google Play and Apple App Store estimate users' gender based on what apps they download?
I would say, the choice depends very much on what data you have and what is your purpose. A few "rules of thumb".

Random Forest is intrinsically suited for multiclass problems, while SVM is intrinsically two-class. For multiclass problem you will need to reduce it into multiple binary classification problems.

Random Forest works well with a mixture of numerical and categorical features. When features are on the various scales, it is also fine. Roughly speaking, with Random Forest you can use data as they are. SVM maximizes the "margin" and thus relies on the concept of "distance" between different points. It is up to you to decide if "distance" is meaningful. As a consequence, one-hot encoding for categorical features is a must-do. Further, min-max or other scaling is highly recommended at preprocessing step. 

If you have data with $n$ points and $m$ features, an intermediate step in SVM is constructing an $n\times n$ matrix (think about memory requirements for storage) by calculating $n^2$ dot products (computational complexity).
Therefore, as a rule of thumb, SVM is hardly scalable beyond 10^5 points.
Large number of features (homogeneous features with meaningful distance, pixel of image would be a perfect example) is generally not a problem. 

For a classification problem Random Forest gives you probability of belonging to class. SVM gives you distance to the boundary, you still need to convert it to probability somehow if you need probability.

For those problems, where SVM applies, it generally performs better than Random Forest.

SVM gives you "support vectors", that is points in each class closest to the boundary between classes. They may be of interest by themselves for interpretation. 
