Could someone explain the main benefits for choosing one over the other and the detriments that come with that choice?
They solve different problems, LinkedHashMap does a mapping of keys to values, a LinkedHashSet simply stores a collection of things with no duplicates.
A linked hash map is for mapping key/value pairs -- for example, storing names and ages:
Map<String,Integer> namesAndAges = new LinkedHashMap<String,Integer>();
namesAndAges.put("Benson", 25);
namesAndAges.put("Fred", 19);
On the other hand, a linked hash set is for storing a collection of one thing -- names, for example:
Set<String> names = new LinkedHashSet<String>();
names.add("Benson");
names.add("Fred");