Actually, the model and manufacturer information is stored in the TIFF data rather than the EXIF data (at least on the iPhone). If the TIFF data is present, then follow these instructions to extract that data, more especially the model, as a string:
NSString *myPath = [[NSBundle mainBundle] pathForResource:@"IMG_0002" ofType:@"jpg"];
NSURL *myURL = [NSURL fileURLWithPath:myPath];
CGImageSourceRef sourceRef = CGImageSourceCreateWithURL((CFURLRef)myURL, NULL);
NSDictionary *metadata = (__bridge id)CGImageSourceCopyPropertiesAtIndex(sourceRef, 0, NULL);
NSDictionary *TIFFdata = [metadata objectForKey:(__bridge id)kCGImagePropertyTIFFDictionary];
NSString *model = [TIFFdata objectForKey:(__bridge id)kCGImagePropertyTIFFModel];
The model number on my iPhone 5S is "iPhone 5S," so you can probably anticipate that it will be "iPhone 6" on an iPhone 6.
NOTICE: If you have the image as a UIImage, avoid obtaining the data by performing UIImageJPEGRepresentation because you will lose much of the TIFF as well as a significant amount of metadata.