There are several factors to consider:
How much time are you willing to invest in moving the thorns?
Your own strength?
The machete is more likely to killing the live plants, whereas the caveman club is not. The caveman club is more likely to crush the old vegetation and push the live plants down and out of the way. You can then step on the plants instead of cutting them up.
The club can be heavy depending on the weight you have. But that is great for exercise, plus you are fueling yourself with the berries you eat anyway. You can use that new strength you develop to use as defense for protecting yourself later in the future.
A machete is very dangerous to swing. You can put a big gash in yourself with an accident. Whereas a club with leave you with a bruise more than anything. Although, your swings with a club will also be safer since you may be more likely to use the weight of the club to push the extra vegetation in a downward fashion.
With a machete, you can hack and slash in all directions freely. This leaves you more vulnerable to making accidental swings, especially with moves that you are not as comfortable with.