There is very little difference - if any - between the general Sephardi way of wearing tephillin and the S&P way. Both have evolved somewhat over the generations, but only in very minor details.
Of far more import are the big changes that have been made in tephillin generally (both Sephardi and Ashkenazi), partly due to improved methods of manufacture (which are welcomed), but also partly due to the mass acceptance of unnecessary strictures that have increased the overall size of the boxes and thickness of the straps - as well as tending to erode the quaint and perfectly legitimate differences between communities.
The illustration by non-Jewish artist Bernard Picart, though not accurate, certainly resembles the second photo below rather than the first (note the straps to and from the index finger).
Note: Picart's illustration shows the tephillin worn on the right hand. I have inverted it so it can be more easily compared with the photos below, which show tephillin worn on the left hand, as is correct for right-handed wearers.
Like all Sephardim the S&P wind the strap outwards over the arm, and back in under it (Ashkenazi custom is to wind the opposite way: outwards under the arm, and back in over it - which leads to a well-known, politically incorrect quip at the expense of the latter that I will not repeat here). Note, however, that Picart's illustration does not show seven such windings. Lovely as the number seven is, seven windings around the arm was never - and is not - a requirement. One simply winds till one gets to the wrist, using as many windings as necessary. Therefore Ben Ish Hai's dilemma as to whether to count the half-winding at the top as one of the seven - and his decision to add yet another winding "to be sure" - becomes irrelevant. But if you like seven windings - that's lovely.
The difference between the groups of Sephardim occurs after the index finger:
A third custom
The main point to make here is not a particularly S&P one. It is that virtually all Sephardim and Ashkenazim used to use a type of knot that looked like a square made of 4 smaller squares (left). This was referred to as a Hebrew letter Dalet, because the lower straps come out of it at right angles, like a Dalet.
The reference in the sources to a "Dalet-shaped knot" was misunderstood, and eventually led to the invention of a new and unwieldy knot that indeed itself looks like a Dalet (right). Many people who originally wore the old knot have now changed to the new one (or been changed to the new one by overzealous soferim without their knowledge), under the erroneous impression that it is the authentic "Dalet-shaped knot" - which it is not (knot).
Arm
Picart's illustration shows the arm tephillin placed too low. The correct position is in the middle of the bicep, on one's weaker arm.
Head
Picart's illustration at the top of the page presents us with another problem. He shows a tricorn hat worn along with the head tephillin, which is significantly lower on the forehead than the position recommended in traditional sources: the natural hairline.
So, either they wore their head tephillin (as in the picture), lower than tradition tells us to, or perhaps the picture is inaccurate and they wore the tephillin in the traditional position with their tricorns tipped back.
In New York today, the soft hats worn by the clergy and congregants can be tipped back, allowing for tephillin to be worn level with the hairline. In London, where stiff top hats replaced tricorns long ago as the only hats worn in synagogue, they are today done away with altogether on weekdays, but a few decades back they were in fact worn precariously tilted back to allow for the correct positioning of head tephillin.