Best speeds will always be provided by using Ethernet cabling rather than Wi-Fi, PROVIDED your Ethernet cables have all eight conductors present, which allows them to jump up to Gigabit Ethernet speeds. Otherwise, you will be limited to 100 Mbits/sec Ethernet.
Your early 2013 Macbook Pro has three internal antennas, and was sold as capable of up 802.11n and up to 450 Mbytes/sec, under ideal conditions including using all 3 antennas. This typically requires being very close to your Router with no intervening dense walls or other objects, and using a 40 MHz data channel, typically on the 5GHz band.
The latest Routers have a much wider antenna spacing and better Signal Processing, so they can provide some modest speed improvement because they are a bit sharper, NOT because they make a leap into new technologies. The new technologies of Wi-Fi 6 are included, but you can not access then from your older MacBook.
{Router upgrades presents a similar dilemma to upgrading the components in your component stereo system. The full impact of upgrading to an excellent component is not seen until you upgrade some other components as well.]