17 November 2016: I apparently noted but forgot to add this excellent description of empennage detail differences: http://phantomphacts.blogspot.com/2014/05/differences-between-phantom-fg1-and-fgr2.html
11 October 2015: Added additional information about engine inlet change
10 October 2015: Added nose landing gear illustration of difference between J79 and Spey F-4K/FGR.1 Phantom
21 February 2014: I added a comparison of the difference between the boundary-layer-removal hole patterns on the forward variable ramp.
15 December 2013: I added some more information on the fuselage changes and the afterburner shroud.
13 December 2013: I added some information about the F-4K changes required so it fit on the elevators of the British carriers.
11 December 2013: I revised the comparison of the area aft of the afterburner nozzle to show that the absence of a "step" in the upper line of unpainted metal was on the prototypes XT595 and 596 and the first production F-4K, XT857 only. The M prototype retained the step.
Note that I refer to the Spey-powered Phantoms as the F-4K and F-4M instead of FG.1 and FGR.2 respectively, the proper British designations.
The key points are these:
1. Air inlet width increased by three inches on each side (Derek Bradshaw). Note that the original inlets were about 43" deep and each had an inlet area of 500 square inches. Widening an inlet by only three inches would increase the inlet area by about 25%, somewhat more than the reported increase of 20%.
2. Afterburner shroud outside diameter of 43 inches; diameter of shroud at aft edge, 38.5 inches (from the circumference measured by Rob as reported on Britmodeler)
3. Wider and higher "nacelles" (bulkhead comparison drawings from Craig Kaston)
3. No change in wing span: the location and width of the trailing-edge flaps did not change and their inboard edge established the width of the F-4K/M fuselage at that point (as measured, the F-4K/M fuselage was slightly wider at the trailing edge of the wing)
4. No change to fuselage aft of the arresting hook attachment except that the outer mold line of the heat-resistant shingles was lowered and extended forward to fit the Spey afterburner shroud.
5. Increase in angle of incidence of the engine installation from 5.2 degrees (J79 measured on McDonnell drawing) to 6.75 degrees (F-4K/M specification)
6. The aft Sparrows were mounted the same distance apart as in the J79-powered Phantoms but were angled at 3.75º nose up consistent with the increase in depth of the lower aft fuselage
Note: It has been reported that the F-4K/M stabilators had reduced anhedral. This is incorrect; they had the same anhedral as every other Phantom.
A common error is to assume that the lower auxiliary air doors on the F-4K/M are in the same location as on the J79-powered Phantoms; they are not. See bottom view illustration.
I've used McDonnell-generated data, three-view drawings, lines drawings, and illustrations to create the comparison shown below, using the pretty-good McDonnell Blue Angel F-4J drawing as a baseline. Unfortunately, although it otherwise adheres pretty closely to the McDonnell B/J lines drawing, it is not exactly correct with respect to the longitudinal location or size of the J79-GE-8 engine afterburner.
An excellent set of walk-around photos of F-4M (FGR.2) XV497 by Graham Platt can be found here: http://www.britmodeller.com/forums/index.php?/topic/234949864-mcdonnell-fg1-fgr2-phantom/
Although photos have limited use in establishing much more than basic shape or position relationships, this picture of XT-595 is as good a side view as you'll see:
The Spey was bigger around than the J79 because it was a bypass engine and had a higher mass flow. The air inlet and engine "nacelle" were enlarged accordingly, the former in width and the latter in width and height. Since the relationship of the thrust line to the location of the airplane's center of gravity is pretty important and McDonnell apparently didn't want to change the location of the arresting hook or make any significant changes to the fuselage aft of station 515 (subcontracted for the F-4K/M to Short Brothers), the Spey had to be installed at a slightly greater angle than the J79, requiring a deepening of the lower aft fuselage. (Other considerations as to engine location were the weight/cg of the Spey versus the J79 and the effect of the exhaust on the flow field around the stabilator.) Close examination of photos leads me to conclude that the top of the Spey's afterburner shroud was located at or very slightly below the top of the J79's afterburner and the inboard sides of the two engines were probably the same distance from the fuselage center line (note the weasel-wording).
The afterburner shroud moved aft to position the afterburner "petals" fully open for afterburner operation and forward when the afterburner was shutdown.
The red area in the following illustration corresponds to the dip in the fastener line in the next illustration.
A fairly direct comparison of a J79-powered fuselage with the F4K/M was obtained from the Robert F. Dorr collection:
Another example is this side-by-side picture taken aboard Independence in 1975:
Another set of changes required for compatibility with the British carriers was a folding radome and shorter fuel vent.
The fuel vent was shorter and the outlets modified into a shallow "V".
I think the bottom line is that modifying an F-4J kit into an F-4K or F-4M model is doable but may involve more changes to the fuselage than most would want to make. Frank Mitchell is not one of those people: http://hyperscale.com/features/2002/fgr2fm_1.htm
"Chek" brought another difference to my attention that I hadn't noticed. The hole pattern on the forward variable ramp (the holes suck off the slow-moving boundary layer air) is different between the F-4B and subsequent J79-powered Phantoms and the Spey-powered ones:
The inlet ramp and inlet itself were changed as well. Because the inlet was widened by three inches, its lip was moved aft about four inches to keep the shock off the leading edge of the fixed ramp properly positioned on it at supersonic speeds. Moving the inlet lip back necessitated moving the leading edge of the variable ramp (which was hinged to the trailing edge of the fixed ramp) back about three inches for the same reason. This meant that both the fixed and variable ramps were slightly wider.