Yes, ehternet is always faster than wireless.
Your 1gbps ethernet cable is actually 1gbps transmit PLUS 1 gbps recieve so it is 2gbps in reality. So your 1300 mbps wifi band (even if you got the theoretical max lab speed) is still slower then etherent.
Now to your question at hand:
The best solution is to run an in-wall rated etherent wire up the wall through attic/crawlspace to the wall your room is it. Now depending on layout of home this can be very very difficult, and of course if this an apartment or other place your rent then you are not allowed to do that anways.
Next best option is to get an av1000 (or better) powerline adapter kit. These plug into your wall socket (not a surge protector, not a power strip but direct inot wall outlet) and then you connect the adapter to router with ethernet, and then connect the other adapter wtih ethernet to your computer/