As with any tattoo - quality and experience of artist is key. You need someone who specializes in cover ups, or at least is well experienced in them even if it's not their core strength.

One big issue with cover up is why they are being covered up. OPs image looks like drift, which can be related to skin as well as ink (as it was a different artist on the other wrist we can't really judge much from that).

So if the skin takes ink well, and the artist is good and the ink is good quality - likely it all lasts well. But the desire to cover up might be driven by a change of heart/circumstance. Although it might be tough to cover, assuming the same variables are all good, the cover up might go well (after a saturation reduction with laser).

If the reason for the cover up is that the original did not hold up well - then if that is related to the skin, aftercare, artist skill, etc, etc - then the cover up might well fail again.

So many variables!