A split is just some housekeeping that doesn't change the market cap though, whereas a rights issue is them raising more capital.
It's just a way to issue more shares that gives existing investors a chance to avoid dilution. In principle it only matters for control (if you want to own x% for voting purposes), if the issue changes the price of your existing shares, or if the exercise is at a substantial discount.
In theory if the money raised is just added to the value of the company, it shouldn't change the price. Depends on everyone else's opinion of their plans for the money raised though.