The slightly 'lower' gearing of the 883 will help more on 1/8th mile runs than a full quarter mile.
You will wind through each gear slightly quicker, but you also have to shift quicker. Years ago there were a number of articles dealing with the gearing in high performance drag cars. Most of these tests involved a car that made a pass with a certain rearend gear ratio (say a 4.10), and then a pass with a ratio in the 3.55 range. The results were very close, much closer at the end of the quarter mile than many would suspect.
The ideal situation is to have your bike (or car) geared so it will cross the quarter mile mark at the top end of it's power band in it's top gear (without shifting into 'overdrive' which is less than a 1 to 1 ratio).
Anyway, LoL, to answer your question, it would depend on the "883 to 1200" conversion that is done to the bike.
There is more of a difference between the 'stock' 2004+ 1200 engines than just additional displacement.
The 883 has a bore and stroke of 3.0"x3.8", while the 1200 is 3.5"x3.8", but the 1200 also has lighter piston and rods, and the useable power range has been increased to 6,000 RPM.
The 883 runs a 8.9-1 compression and can run on 87 octane fuel, while the 1200 has a compression ratio of 9.7-1 and requires 91+ octane fuel.
The 1200 also uses high flow cylinder heads from the Buell XB line, and cams from the 1200 Sport.
Factory horsepower and torque figures for the 883 are 53 HP at 6,000 RPM, and 51 LB-FT at 4,300 RPM.
Factory horsepower and torque figures for the 1200 are 70 HP at 6,000, and 79 LB-FT at a lower 3,500 RPM.
The extra displacement, different rods, heads, and cams all need to be replaced in the 883 to do a "true" 883 to 1200 conversion. Another thing you might have to consider during a conversion is raising the rev-limiter on 883 bikes. We hooked some gauges up to my 2005 1200C and the rev-limiter kicked in right below 6,000 RPM. On a friends 883 it kicked in just over 5,500 RPM.
Stage 1 dyno tuned 1200 bikes usually see rear wheel horsepower figures in the 70 range, although I have seen higher figures where everything came together just right.
Quarter mile times for a well tuned "Stage 1" 2004+ 1200 vary, depending on the rider, ideal conditions, etc., but they should be somewhere in the very low 13 second range for the most part.