Ok,i will get flamed for this but:
The A4000 is full 32bit across the board, the 1200 is not.
The A4000/040 blows the 1200 away stock machine to stock machine and here is why.
Internally a CDRW or DVD-RW,2 hd's and 2 floppies fit the A4000- The A1200 gets 1 HD and 1 floppy (yea,i know,u can hack a laptop dvd-rw internally) but this is hacking.
The A4000 comes with a decent 150W psu. A1200 is a crappy 20~ watt psu.
the 1200 is actually wider than the 4000,but not as deep or tall, so you could call that a draw.
the A4000 is AGA also
You can set a monitor on top the 4000.
The A1200 is 020EC(no mmu/fpu) 14mhz with 2MBram,the A4000 is 040/25 with full mmu/fpu 16MB ram on the motherboard.
comparing stock to stock machine, the A4000 ide is faster(040 helps),the ide in the 4000 is at least buffered.
You can technically make a A4000 quite a bit faster than the 1200 with the csppc. 604/233 blows the 603/240 out of the water.(not withstanding guys hacking bliz boards,i'm talking stock parts here).
CSPPC UWscsi screams,it pushes 20+MB/s on the crappies drives.blizzard is scsi2(10MB/s if your lucky).
The A4000 stock has a proper expansion bus,zorro3, not crappy slow clock ports and 50 dongles hanging off stuff to make it decent.Even the A1200 FastATA and such is a cpu pig,while the csppc scsi cranks along at full speed with low cpu usage(even a CS MKIII).
If you want to compare mediator in both models,the 1200 loses again for speed, its transfer window to the board is smaller i.e. slower..
The A4000 is easy to install a pal/ntsc switch also,so you can permanently switch easily between pal/ntsc-just 2 wires with switch to the jumper.
The A4000 comes with a clock.
A 16MB A4000 with stock 040 card(even the crappy A3640) is a way way way faster machine out of the box than a stock A1200,and still a bit faster than the 030/50mhz boards in the 1200(yes theres 040/060 boards,but dont forget the prices!). and as far as cost, expanding a 1200 these days just to meet the A4000 usually costs as much or more.
The A1200 pcmcia is a winner tho,very handy for cheap ethernet or Pcmcia/cf,i will give it that hands down.
A zorro3 deneb though will out do the subway in a 1200 speed wise by quite a factor.if u want to do this, you could argue a $5.99 ehternet dongle is the way to go in the A4000 and will be faster than 1200 pcmcia ethernet.you also get USB2 and a flashrom to install a ton of stuff in.The deneb would only run on the 1200 with a zorro board/mediator addon in slow z2 mode(2-3MB/s?).
The 1200 also wins portability,but then again the bulky psu is not convienient and should be counted,the A4000 psu is at least self contained in the box.The A4000 comes with a real on/off switch on the machine 
There a indivision for the 4000 also.
If u price a expanded 1200 and a used 4000,i bet you the price comes out close(and i dont mean if someone gave u a pile of stuff free).
Basically you can get a 1200 and add a small fortune in slower periphrials to it,and have dongles popping loose half the time,or a box stock a4000/040 you dont have to add 50 things to.
So in conclusion half you people either never owned anything but a 1200 or don't compare specs worth beans
the information is out there plain as day.
Mike
A1200 was to be sold to people who wanted to mainly play games and maybe play with Dpaint or a music tracker
And the A4000 had the same identical barely adequate chipset called AGA
So in that sense the A4000 was overpriced too, AGA was just a catch up to VGA too it was in no way superior to mid 80s PCs like when A1000 came out Vs EGA + Adlib soundcard + 8086 XT. AGA still had 8bit sound, was still a 16bit chipset really, had a dodgy HD floppy drive controller where the data is slowed down to the speed of an 880k to read it in, hugely expensive with expansion of a PPC card, a proper 24bit card, a 16bit sound card etc etc.
A4000/030 was a real donkey of the range.