You betcha. Keep doing as many object comparisons as you can using the .equals method, and you're good to go. Use the comparison operators primarily for primitives or when you actually want to compare objects for identical check. Equals is defined from the core object, so you can easily override and define your own handling.
Two interfaces to look at as well are the Comparable interface which will grant you the
int compareTo(T); method, and the Comparator interface which will grant you the
int compare(T, T); method. These can both be used for equality check, as the result of the "same" object would be 0 in either of these, but are also useful for using Collections as the sorting algorithms will make use of the Comparator, or you can usually provide the sort with a Comparator.