Just a basic overview of the Tumi 19 Degree Aluminum Continental Carry-On and Away's The Carry On: Aluminum Edition:
Both brands hold 35L of cargo, using an aluminum frame closure secured by two case hinges and two TSA-approved combination, push locks.
Tumi's version is a full 1.0 lb heavier than its Away counterpart, 11.7 lbs vs. 10.7, respectively.
There is nothing extraordinary about either manufacturing processes. Both cases are imported and manufactured overseas, as opposed to Zero Halliburton aluminum cases that have shifted back to American resourced materials or RIMOWA trollies exclusively made in Europe and Canada.
The diagonal wave molding on the Tumi 19 Degree line hides wear and tear better, IMO. The diagonal grooves can visually minimize the appearance of scuffs and scratches that all aluminum luggage encounter. The horizontal lines of the Away Aluminum series make wear and tear more visible, especially with its visually smooth surface.
Build quality, I would go with Tumi. With over 120+ patents in the luggage industry, Tumi has the provenance of generating in-house solutions to introduce to its available products. Away, however, is the new kid on the block. With many of its components and designs, resourced elsewhere (think Hinomoto wheels on its trollies, and YKK slide fasteners), the brand has not yet evolved into in-house innovation. Instead relying on already existing technology that is generic among the industry.
I would easily go with either brand, both solid choices for aluminum luggage.
However, if I had to pick, Tumi 19 Degree Aluminum, for sure.