How do you make flush cuts to a precise depth?
Since you're insulating and dry walling this "shed", you may want to treat it as an additional room, where extra insulation would go a long way toward your comfort. 

Although it's possible to rip 1.5" off the edge of the 2x6 with an oscillating saw, you're likely to burn through several blades, and possibly a saw or 2 doing it. It'll be much easier to add 2x2 furring onto your 2x4 studs to make up the thickness. If you're insulating and dry walling, this would also let you add more insulation for a more comfortable room with only minimal cost and labor.

For more strength, in addition to insulation, if you have 2x6 top plates also, you could sister in 2x6 studs or add offset 2x4 studs between the existing ones for a double- stud wall.