What you are seeing is called "stitching." its an artifact of the transparency flattening happening during the export (PDF/X-1a flattens transparency). It generally doesn't show on press output.
Stitching can be avoided if you export PDF/X-4 and no EPS are used.
The very nature of PDF/X-1a or even PDF/X-3 requires that any transparency, including transparency effects such as drop shadows, clipped images, feathering, glows, embossing, etc., be flattened into opaque objects at the target device's resolution and in the target device's process CMYK color space. Such flattening introduces boundaries between the resultant opaque objects. Those boundaries often show up on screen and sometimes show up in print as very thin white lines.
The industry has advanced dramatically since PDF/X-1a and PDF/X-3. All modern-day RIPs can indeed support PDF/X-4 with live transparency and color management using native PDF rendering (no stink'in PostScript intermediaries). Print service providers who refuse PDF/X-4 either (1) have ancient RIPs and workflow practices, (2) are ignorant of the capabilities of their systems, (3) are arrogant (“my way or the highway”) Luddites, or (4) some combination of (1), (2), and (3).
Adobe most strongly recommends use of PDF/X-4 for reliable PDF publishing workflows.
PS: EPS is only a significant issue if the EPS contains flattened transparency!