Steps to reproduce:
1. Open User's attached project "Test 5.5" with Unity 5.5
2. Make sure Platform is set to iOS
3. Have a look at the texture. Notice the box compression pattern
4. Open User's attached project "Compresion Bug Unity 5_3 Project" with Unity 5.3
5. Make sure Platform is set to iOS
6. Compare the texture with the previous one

Expected behavior: textures look the same
Actual result: artefacts appear - textures look different

Reproduced with: 5.6.0b8, 5.5.1p4, 5.4.4p3
Not reproduced with: 5.3.7p2

Note: if Platform is set to Standalone or Android, textures look the same. The difference is also visible in 5.4.

Workaround: the issue is gone if Max Size is changed to 2048 or higher for the specific texture under Compression settings.

Fixed: Select texture, in Inspector: Select Platform: iOS, Change Resize Algorithm to Bilinear.