CAT 5E and CAT 5 (which is probably what your older cable is) will yield nearly identical results on data transfer with your 100mbps router. CAT 5E, however, would be the minimum requirement should you step up to a Gigabit router.
You never stated what your transfer speeds were, but a lot of other issues could also affect that speed such as older, slower HDDs. I can say with almost certainty that homeplugs will be quiet a bit slower.
Also, as you may already be aware, 100mbps on router is not the same as MBs on file size. The max speed of your router would be 12.5 MBs per second. 8 bits per byte.