Is there a difference between using a BTC mixer vs just Swapping BTC to XMR and then to whatever currency you want.
Yes. When introducing XMR in the equation, you're most likely going to receive better levels of anonymity. The reasons why you might want to use a mixer over XMR swap are: comfort and pricing.
Once it has been converted to XMR, it is private correct?
Correct. If you run a Bitcoin full node, a Monero full node and make the exchange through Bisq, then you're achieving the highest levels of privacy there are.