Firstly, I assume that when you say "tube" what you mean is Hollow Structural Sections, and when you say "pipe" I assume that you mean typical scheduled pipe sections.
In the US, the AISC Code specifies material properties for structural shapes. From the manual Tables 2-4, we can see that the Pipe material is ASTM A53 Gr. B, and that for round HSS we have ASTM A500 Gr. B as the most common shape.
These two materials are characterized by their yield and tensile stresses.
For A53 Gr. B, Fy = 35 ksi and Fu = 60 ksi.
For A500 Gr. B, Fy = 42 ksi and Fu = 68 ksi.
Not only is the pipe wall thickness and pipe ID/OD part of the strength of a given element, but also the Material Strength plays a large roll.
Your intuition that the wall thickness and ID/OD effect the strength is correct. But if you have a pipe with identical dimensions as an HSS tube. The HSS(tube) will be stronger because it has higher Fy and higher Fu.