The output of Graphics3D looks blunt (polygon borders, arrow) when a polygon primitive is present in the scene with texture that has opacity channel. Also it seems that different kind of texture filtering is applied. I'm on Win10 and tested the code on 2 different PCs with GPUs from different vendors. I'm also interested in boosting the overall image quality like aliasing and texture filtering. Thank you!
SeedRandom[0]
imgData = RandomReal[1, {4, 5, 3}];
Image[imgData]
Graphics3D[{{Texture[Image[imgData]],
Polygon[{{-1, -1, -1}, {1, -1, -1}, {1, 1, -1}, {-1, 1, -1}},
VertexTextureCoordinates -> {{0, 0}, {1, 0}, {1, 1}, {0,
1}}]}, {GraphicsComplex[{{1, 0, 2}, {0, 1, 2}, {-1, 0,
2}, {0, -1, 2}},
Polygon[{{1, 2, 3}, {3, 4, 1}}]]}, {Arrow[{{0, 0, 0}, {1, 1,
1}}]}}, Boxed -> False, Lighting -> "Neutral",
ViewPoint -> {1/2, -2, 1}]
Graphics3D[{{Texture[Image[Map[Append[#, 0.5] &, imgData, {2}]]],
Polygon[{{-1, -1, -1}, {1, -1, -1}, {1, 1, -1}, {-1, 1, -1}},
VertexTextureCoordinates -> {{0, 0}, {1, 0}, {1, 1}, {0,
1}}]}, {GraphicsComplex[{{1, 0, 2}, {0, 1, 2}, {-1, 0,
2}, {0, -1, 2}},
Polygon[{{1, 2, 3}, {3, 4, 1}}]]}, {Arrow[{{0, 0, 0}, {1, 1,
1}}]}}, Boxed -> False, Lighting -> "Neutral",
ViewPoint -> {1/2, -2, 1}]