Is installing packages with apt-get faster than apt?

Installing packages with apt-get is not faster than apt. apt and apt-get both download from the same update server (whatever update server mirror you selected) at the same download speed.

From the accepted answer to What is the difference between apt and apt-get?:

apt-get may be considered as lower level and "back-end", and supports other apt-based software tools. apt is designed for end users and its output may be changed between versions.

No, apt is an interface for apt-get. They both have the same speed. apt is not CLI stable. Speed depends on the Download server. Look this answer for more detail. If you want a better speed you can use apt-fast.

This website may help.

Before Ubuntu 16.04, users regularly interacted with the APT package manager through the use of command-line tools: apt-get, apt-cache, and apt-config. Although these tools offer many functionalities, most average users did not utilize all of the commands they provide.

Therefore, Linux wanted to create a simplified tool that only consisted of essential commands. With the release of Ubuntu 16.04 and Debian 8, they introduced a new command-line interface – apt.

The main goal for this novelty was to merge the most commonly used apt-get and apt-cache commands under the same command prefix.