I may be mistaken, but I think the 1100 Competitions have overbored barrels with a longer forcing cones and the 1100 Classic traps have more conventional dimensions.
( Kind of like the difference between Beretta's Mobil & Optima chokes or Browning's Invector & Invector Plus chokes, i.e., "different bore diameters before the constriction
taper of the chokes start".
I don't believe they are interchangeable.
From the patterning I have done ( literally hundreds of patterns ) with both Beretta & Browning and measuring choke length & constriction, I don't personally believe, constriction for constriction ( i.e., comparing say "Modified" with "Modified") there is any meaningful or noticeable difference between Mobil/Optima or Invector/Invector Plus choke performance.
I can't honestly comment on Remington choke performance other than the Classic barrel/choke performance, but would hesitate to say the Competition chokes performed noticeably
better either ! The difference is that both are meant for different barrel bore configurations. Certainly, despite the brand, one is not "more accurate" than another.
What I have noted amonst the brands is that generally, overbore barrels with longer forcing cones seem to generate less felt recoil, and that the long conical parallel taper chokes
seemingly have slightly denser cental shot distribution ... but "Modified" means "Modified" ... roughly an actual 60% shot charge distribution in a 30" circle at 40 yards ... regardless
of what the choke migt be labelled. I have seen chokes from various manufacturers, whether original or aftermarket, labeled "Improved Cylinder" for example, that consistantly
printed weak "Skeet" through to almost "Modified" pattern percentages, even with different brands of ammunition and reloads. A buddy has a Briley/Browning Invector Plus style choke
that is labeled "Cylinder" that throws very strong "Modified" patterns.
Beyond all the manufacturer's and aftermarket choke makers hype, it all comes down to what your particular barrel & choke combination will produce with a specific brand of ammunition or your favourite reload. Supposedly identical barrels of the same make and smae choke will often produce markedly different results with the same choke, and often barells will seem to
produce dense more evenly distributed patterns with one shot size over another. The only way to find out is pattern, pattern, pattern !