EF

public void UpdateEntity(ParentItem parent)
{
    // Load original parent including the child item collection
    var originalParent = _dbContext.ParentItems
        .Where(p => p.ID == parent.ID)
        .Include(p => p.ChildItems)
        .SingleOrDefault();
    // We assume that the parent is still in the DB and don't check for null

    // Update scalar properties of parent,
    // can be omitted if we don't expect changes of the scalar properties
    var parentEntry = _dbContext.Entry(originalParent);
    parentEntry.CurrentValues.SetValues(parent);

    foreach (var childItem in parent.ChildItems)
    {
        var originalChildItem = originalParent.ChildItems
            .Where(c => c.ID == childItem.ID && c.ID != 0)
            .SingleOrDefault();
        // Is original child item with same ID in DB?
        if (originalChildItem != null)
        {
            // Yes -> Update scalar properties of child item
            var childEntry = _dbContext.Entry(originalChildItem);
            childEntry.CurrentValues.SetValues(childItem);
        }
        else
        {
            // No -> It's a new child item -> Insert
            childItem.ID = 0;
            originalParent.ChildItems.Add(childItem);
        }
    }

    // Don't consider the child items we have just added above.
    // (We need to make a copy of the list by using .ToList() because
    // _dbContext.ChildItems.Remove in this loop does not only delete
    // from the context but also from the child collection. Without making
    // the copy we would modify the collection we are just interating
    // through - which is forbidden and would lead to an exception.)
    foreach (var originalChildItem in
                 originalParent.ChildItems.Where(c => c.ID != 0).ToList())
    {
        // Are there child items in the DB which are NOT in the
        // new child item collection anymore?
        if (!parent.ChildItems.Any(c => c.ID == originalChildItem.ID))
            // Yes -> It's a deleted child item -> Delete
            _dbContext.ChildItems.Remove(originalChildItem);
    }

    _dbContext.SaveChanges();
}


//---------------------------------------------------
//---------------------------------------------------

var parent = context.Parents.GetById(1); // Make sure that childs are loaded as well
foreach(var child in modifiedParent.ChildItems)
{
    var attachedChild = FindChild(parent, child.Id);
    if (attachedChild != null)
    {
        // Existing child - apply new values
        context.Entry(attachedChild).CurrentValues.SetValues(child);
    }
    else
    {
        // New child
        // Don't insert original object. It will attach whole detached graph
        parent.ChildItems.Add(child.Clone());
    }
}

// Now you must delete all entities present in parent.ChildItems but missing
// in modifiedParent.ChildItems
// ToList should make copy of the collection because we can't modify collection
// iterated by foreach
foreach(var child in parent.ChildItems.ToList())
{
    var detachedChild = FindChild(modifiedParent, child.Id);
    if (detachedChild == null)
    {
        parent.ChildItems.Remove(child);
        context.Childs.Remove(child); 
    }
}

context.SaveChanges();