What is the converter for? Connecting to the laptop, or connecting to the monitor?
Does the monitor use DVI or VGA? Yes DVI is significantly better than VGA. It is the nearly forgotten red headed step brother of the HDMI cable. If the monitor uses VGA only though, a converter isn't going to help.
If the monitor uses VGA, you will need a miniDP to VGA adapter. If the monitor uses DVI you will need a miniDP to DVI adapter.