So I've never used desktop so cannot speak intelligently on what QBO does not have that QB Desktop does have.  As you mentioned, the CC'ing bit around invoicing is a massive step backwards.  

Another BIG thing for me: if your invoice upload has a negative number in it, it breaks.  So, like i mentioned, i invoice about 200 invoices a month, and I use the upload feature ofc because it's otherwise untenable.  If a client has a credit, or a 10% discount, or whatever, I cannot add a negative line item to the invoice.  It's such an inconvenience as I have to go into pretty much every invoice and negate positive numbers that should be negative, completely reversing the benefit of the template upload.