Which value to compare for deciding thickness of a pressure vessel.

You need to know the detailed analysis methods appropriate for this type of tank. Are you going to use closed form sizing or FEM analysis?
And you need to know what design code or customer requirements are applicable to determine design and sizing requirements and factors of safety.
And you need to know the usage requirements for this tank - spacecraft one time use? ground tank used multiple times which might be sized by fatigue? other?
There is way too little info to be able to reply with any details.

so you want to make a new gas tank (reinventing the wheel ?). The current tank would have shell of some thickness and some yield strength.

Would the new tank be the same size as the old one ?

Research "hoop stress". This is the stress in a pressure vessel, and compare this to yield stress (including whatever safety factors you need to).

As for the thermal properties of the liner, the same logic applies ... compare with the current tank. You should aim for the same performance and improve on the current design in some way (cheaper ? higher working pressure ?? domestic production (if you don't want to buy from overseas) ??)

"Hoffen wir mal, dass alles gut geht !"
General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.