engine.PublishingContext.ResolvedItem.Item.Id
You can also check the Publishing Context's resolved Item and see if it's a Page or not (if it's not, then it's a Component).
For example:
Item currentItem;
if (engine.PublishingContext.ResolvedItem.Item is Page)
{
currentItem = package.GetByName(Package.PageName);
}
else
{
currentItem = package.GetByName(Package.ComponentName);
}
TcmUri currentId = engine.GetObject(currentItem).Id;
If you want to shortcut the engine.GetObject() call, then you may be able to get the ID from the Item's XML directly:
String currentId = currentItem.GetAsSource().GetValue("ID");