ASUS RT-68 vs RT-AC56

If you check on the FCC website using the FCC identifier for each, the 68U has significantly higher power output rating for its 2.4 and 5GHz radios:

The 68U lists .63 and .73 watts while the 56U lists .34 and .5 watts for the 2.4 and 5GHz bands respectively so I would expect the likelihood of a better signal at a distance with the 68U.

A quick look at the test charts on them both HERE supports that the 68U is superior for its 2.4 and 5GHz throughput at distance.
 
I read some of your other posts where you got answers from one of our most knowledgeable wireless and networking posters (bill001g). If your house is large, has several floors, or uses very dense building materials, you may benefit more from having a good router and a second good router used as a wireless access point at a distance from your first (main router).

An AP will usually give better results than just buying another, albeit better, router. To set up an AP you need to connect the two by either (1) Ethernet cable, or (2) if that is not feasible use a pair of very good powerline adapters -- I would recommend the AV2 MIMO 1200Mbps rated models as they reach around 200Mbps in the real world.