I am not sure whether my thoughts will be helpful - they certainly aren't a clear answer . . .
Will the Duchesnia grow densely enough to make a good ground cover and keep the weeds out?
Will it look good in dry or wet weather?
The voles in my area (I have a high density of voles) don't eat the catmint, but they will still tunnel around it.
Check out the thread on fall cleanup shortcuts. You may find suggestions of tools to help keep the catmint looking good with less time involved.
Can you keep some of both for a while to see which looks better overall or if both can look good coexisting?
Or should you consider another groundcover entirely to meet your needs for neatness, low maintenance, and not overly encouraging to voles?

Here is a link that might be useful: fall cleanup shortcuts

Catmint is too tall to be what I consider a groundcover. I'm not familiar with the other plant you mentioned. There are oodles of various groundcovers - do a board search and you should find some threads with suggestions.

Hello marymax,
I think it depends: what kind of soil, temperatures in your area. I came across that funny little plant when I wrote my thesis on an old garden near Berlin, botanizing/ making an inventory of all plants, on sandy soil, with dry summer and rather cold winters with little snow.

The Duchesnea grew near shrubs or in an neglected, former lawn/meadow situation.

Under those conditions, I clocked the plant rather as being resilient than competitive. So it kept going when the rest started starving or wilting.

It spreads by stolons, so that it a plus for the groundcover angle.

IMO you can hardly compare it with Catmint (Nepeta?) as the latter is showier, more competitive and much taller.

For semi-shade, and round/ near shrubs on somewhat poor soil they could work. On rich soil with good water supply I would go for something else, like Geranium or Waldsteinia.

Well, enjoy that funny faux-strawberry,
bye, Lin