Receiver design is the main difference...and drives part of the 1,000 to 1,300 USD$ price difference.
Screen size is the same.
The FT-3000 receiver design closely resembles the design of the FT-9000 and FT-5000.
The FT-1200 receiver is an entirely different design.
Like the 5000 and 9000; the FT-3000 uses a 9 MHz 1st IF and 9 MHz center frequency roofing filters. The FT-1200 has a 40.455 MHz 1st IF and center frequency.
The lower the 1st IF frequency, 9 MHz. in this case, enables a better filter design and a tighter pass band of that filter.
The 9 MHz IF will be better at rejecting images....and the overall desired versus undesired signals in the front end of the receiver (first stage right after the antenna).
The roofing filter "sits" at the output of the 1st IF stage's mixer. All signals passing through the roofing filter (desired vs. undesired) will effect the subsequent 2nd and 3rd IF stages, the DSP, and ultimately the quality of what is in the audio passband ( 300-3,000 classic radio communication frequencies).
The long and short of the two radios are the design and performance of the amplifier, oscillator, mixer, and roofing filters. Together as a system these components will effect your dynamic range, minimum discernible signal, compression, linearity, and the ability to manage strong and weak, desired and undesired signals, all side by side on adjacent frequencies.
Sherwood Engineering has an interesting specs / perf' table and PowerPoint on receivers. Take a look: http://www.sherweng.com/index.html
There is the lab bench vs the "hands on" experience in your shack; i.e. operating habits, proximity to strong signals, and the budget for additional amateur "kit".
See if you can find a dealer in the RSA or your travels, that will enable some time in front of today's rigs. ENJOY and HAVE FUN !
'73 Tom N2AXX