I believe you are referring to is related to Pascal's principal "for a fluid at rest in a closed container, a pressure change in one part is transmitted without loss to every portion of the fluid and to the walls of the container". There will be a pressure differential initially in the tanks and the atmosphere along with gravity will "push" the water on one side and "pull" on the other.

Therefor if the parameters for both sides of the tanks and tubes are exactly the same and being at the same elevation they will constitute a closed system with air pushing in on both sides (this assumes that air is at rest). Some diffusion of air into water will happen but this should also be equal. Since we are talking about a liquid and gas the real world scenario would result in the tanks coming close but never to equilibrium. This is the basis for hydraulics by forcing a closed system with a highly incompressible fluid such as water. A tiny air leak and the system can fail!

https://en.m.wikipedia.org/wiki/Water_level_(device)

Water levels makes use of these principles as well.

 

You can make the pipe as narrow and as long as you want and the fluid as viscous as possible. They all don’t matter. Yes, the two tanks will reach the same level because of diffusion.

Fill a balloon with hydrogen and see if it remains inflated over time.

 

I had this query:

Assume two tanks connected by a very very very long pipe...!!

To start with first tank is full... Open to atmosphere...

Second tank is empty... Open to atmosphere...!!

Once we open the interconnecting valve, will the level of the liquid in two tanks become equal, eventually?

What if the liquid is more viscous OR pipeline diameter is small (thereby offering more friction)... Will the level in both tanks would still equalize eventually..??

Thanks & Regards,
Rahul

Assuming tanks are at the same level,
YES

Q and viscosity only has effect with flow,
the more viscous, the slower the fluid will flow,
but it will still eventually flow,