Thanks for all the contributions.
I have now stumbled on another "solution" to supplement the helpful ideas which have been shown.
When the MacBookPro was bought in MARCH 2013 it included in the box a small booklet
"Hello.QUICK START GUIDE Z034-6585-B" which on the first page showed a picture of the MBP connections.
These were Power, Ethernet, FW800, Thunderbolt, USB 3, SDXC slot, Audio in/out.
When I connected the LaCie 3TB back up drive, the connections available were [ fastest first ]
"USB 3.0, eSATA, FW 800, USB 2.0 ".
So obviously I connected the LaCie socket marked "USB 3.0 (USB 2.0 compatible) to the supposed "USB 3" socket on the MBP, expecting the claimed 5 Gb/s transfer speed.
It seemed to work OK, though not mind blowingly fast.
A day or so ago I looked in "About This Mac" and noticed that the hardware listed under USB was merely "USB 2.0 Bus" with max speed as 480 Mb/s.
This conflicts with the Apple "Hello." booklet.
It seems that the "About This Mac" data is more likely to be valid than the booklet.
I have now connected the FW 800 sockets on both LaCie Drive and the MBP laptop, and it seems faster [ claimed 800 Mb/s ].
It would have been faster to use the LaCie sockets for USB 3 or eSATA, but there do not seem to be equivalent sockets on the MBP.
Perfection is not of this world.