well, niether of you has to prove it
to me.
but anecdotes from real life are always interesting and good way to make a technical point.
i'd say to OP
EEG sounds like it will be connected to some living creature, possibly yourself or a friend.
Most obvious trouble with breadboards like this
is wires come loose and flop against something so make DARN SURE there's no high(> about 15volts) voltage on your board.
Second trouble is as already mentioned, on a breadboard the leads will be longer. That causes trouble with noise pickup, every wire is an antenna.
Third trouble is , as mentioned, on a breadboard you can't "guard" sensitive inputs.
This TI datasheet explains that, see section CIRCUIT BOARD LAYOUT AND ASSEMBLY on page 8, and fig 4.
http://www.ti.com/lit/gpn/ina116
Try it and see.
There's several ways to make printed circuit boards at home
i use this one
http://gilmore2.chem.northwestern.edu/projects/garbz2_prj.php
doing the iron-on transfer takes some practice
a Dremel with the drill pess accessory is really handy.
http://www.micromark.com/RS/SR/Product/83453_R.jpg