I guess part of it depends on how much you fax per month, since I believe Updox charges a fee for faxes (4 cents a page over the 500/$20 or whatever plan you pick... and, correct me if I'm wrong, but I think that 500 faxes outbound AND inbound)... and faxing from the Brother is "free" (besides the phone line charge).
I would check to see if your Brother is networkable, and if so, plug it into the network via ethernet cable rather than USB to the workstation. I believe it requires a different installation procedure (when you load the installation software, it should ask you if it's being installed on a network, or local-USB).
After proper installation of my Brother MFC 7820N on the network and stations, the "Brother PC-Fax" is an option printing destination from any of the workstations. Printing to it, the virtual fax machine "image" pops up on my screen and is used as any other fax.
If your Brother is not network-enabled... and you don't want to buy a networked MFC, there are other online fax options.
If not connected to my network, I may use my Onebox account (which is for me is primarily used as a virtual receptionist in place of an on-call service, but has lots of other uses).
A lot of users do like UpDox, and I may go there again one day myself. Would have to assess the pricing package closely though.