Men and women have the same sex hormones, just in different amounts. Men have 10 times more testosterone than women. Women have more estrogen. But women do have some testosterone and men have small amounts of estrogen.
Anterior cruciate ligament (ACL) injuries have actually been linked to changes in hormones. Each hormone plays some role in ligament laxity. Combined together the effect is much greater.
A recent study showed ACL injuries occur more often in women with higher levels of testosterone. However if testosterone is the hormone that increases joint laxity then men would be expected to have more joint injuries.
It's likely the hormones acting together makes a difference. More study is needed to find out more about this.