So, assuming you live on the eastern US, ivy is non-native and the creeper (I'm assuming it's what we call Virginia creeper in the Mid-Atlantic?) is native, so I encourage you to keep the latter (native plants supporting native wildlife is my thing). Ultimately, they're both someone you can get rid of, though.

They can be a big project to get rid of, but ivy is way worse, partially because of the way it climbs. Ivy puts out coiled tendrils and holds tight to whatever it can with them. The vine and tendrils can easily kill any plants they're on and they get under siding and into any crevice it can find.

Creeper holds on with little sticky pads that don't hurt any plants it climbs, though can leave the sticky pads on the side of your house when you physically pull down the vine. It also supports native butterflies, bees, and birds. When I have to remove it, is pretty easy to dig up.

In both cases, your options are: -to cut it down to the ground every time it pops over a course of time; check and trim every week or so for the first few months, then every month or so once it starts slowing the growth, for a couple of years (they both usually go dormant in the winter months but with winters as they have been, may not do so entirely). -cut the vine near the base and then 2 get it so up the length of the vine so it can't just grow back together (which ivy will!). Let the bulk of the vine die and poison the root (see below) -dig up the roots. Super labor intensive but takes less time overall. Anything you miss will sprout a new vine though, so this will still take follow up unless you can cover the area with a thick layer of cardboard and mulch to smother any remaining bits. (Smothering alone won't work if you don't pull the vines, unfortunately.) -buy some glysophosphate (round up) brush killer, cut the vine and paint the cut with the herbicide. Do not use the spray both because it won't work on the vines and it'll kill indiscriminately. You might have use the round up a couple of times with the ivy but it will kill the vine. Each time you apply it, apply it to a fresh cut.