The diference is not much to normal hunting ranges 400 yards or so, but when you start stretching somethings legs, velocity does come in handy. Reloading the 25-06 to max levels puts it around 200-250fps above the roberts, that comes in handy at longer distances.
I cant see how some would say they can shoot a 243 all day, but not a 25-06. The 25-06 dont kick any more then a 243 for a couple reasons. First, the rifles in 25-06 are always heavier, so that will knock recoil a little. Second, if you shoot 100g at 3300fps, its only going 200fps faster give or take then the 243. If someone cant handle 200fps difference in a heavier gun, I think something is wrong personally.
The 25-06 is a great cartridge and I would not hesitate to wack an antelope out to 700-800 yards with it and the 115g NBT. 257 BOB and 243 would poop out around 500-550. Thats the difference between the 3 in my opinion.
Take a 115g NBT at 3200fps which is easily achievable in the 25-06 with reloads and RL-22 or IMR-7828 powder, among others. 3200fps with a .450 BC beats the snot out of factory loaded 117g soft point boat tails at 3000. For one, its going 200fps faster then factory loads, and 2 the BC is greater which only helps you at longer ranges.
Heres a quick chart on the 25-06 w/115g at 3200fps. Sight in 3in high at 100 yards will put you dead on at 295-300 yards. At 400 yards your drop is -9.5, at 500 yards its -24.8, and 600 yards is -47. I think that falls under the category of "flat shooting."