I think the best way to find out is to try it. But I can imaging the lumber having these disadvantages :
1- warping
2- A haven for bugs and insects,
3- compacting the soil ( depending on thickness and water absorption) .

I don't even like the cardboard idea. In my opinion mulch has to be someting that the soil underneath can breath. Plants roots also need some air.
JMO

Seysonn

I might try it on the paths in the bed if there are any but not around the plants themselves. Like Seysonn said - a great hideout for insects and slugs would be in hog heaven. :)

And even cardboard is permeable allowing for both water and air to pass through. Both are very important to the plant and soil health and neither would have access to the soil with lumber.

Plus the roots don't stay in the hole you cut in the wood. They run for feet in all directions. So getting water out to the roots where it is needed would be difficult.

Dave