Well, GL’s image mipmapping will be a little bit different from CoreGraphic’s. But I had a quick run of the demo app’s 2D demo, flipping between GL and CoreGraphics for the static RGB image, and it looks pretty much identical to me.
But you know… I can’t see the rest of your image, but it really doesn’t look like something you should be using bitmaps for. If you’re drawing anything as simple as a rounded rectangle border, the only sensible way to do it is with vector graphics.
Just run the big demo app and choose “Graphics: 2D rendering”. You can swap the renderer at any time by pressing the ‘2’ and ‘3’ keys. Certainly there’s not much control over how GL filters the images, but you could tweak it by nudging it around by sub-pixel amounts, it could just be that CoreGraphics is snapping the position to a pixel boundary differently.