You should ignore considerations about performance at this stage. There is probably no significant performance difference between the two; you can investigate the source code by unzipping the "src.zip" file in your
Java installation folder. Have a look at this
article by Brian Goetz and see what he says about performance. You should use methods for their designed purpose. If there is an equals() method use that for equality and if there is a compare/compareTo method use that for comparisons.
There are a few possible exceptions however. The
BigDecimal equals method returns false if you present 1.0 with 1.00, so you would have to use the compareTo method and == 0.