The AXE132/AXE133 driver boards (which are the ones used on the AXE133Y and AXE134Y OLED displays) will work with either an OLED or LCD. In terms of physical changes, they just need to have the contrast pot fitted if used with an LCD, but if that pot is fitted it still works OK with an OLED display, the pot just doesn't do anything. You do need to edit the driver code for the 18M2 AXE132/AXE133 board to select the display type (OLED or LCD) and also the desired character set. A look at the driver 18M2 code shows how this is done, click here:
http://www.picaxestore.com/index.php/en_gb/picaxe/add-on-modules/axe132.html and then select the "resources" tab and you can download the three sets of code for driving different display types and see how they are adapted.
The AXE033 driver board is different, in that you cannot re-programme it, so there may be issues if it is used with some displays. I've never tried to use an AXE033 driver board with anything other than the supplied LCD, but I do know that not all displays default to the same character set, and unlike the re-programmable AXE132/AXE133 driver boards there is no way to change the character set or display type with the AXE033 board, it's fixed as being an LCD driver that has a single defined character set, I believe.
So, there's no reason why fitting headers to a breadboard and using the same AXE132/AXE133 driver board with different display types shouldn't work OK, as long as you load the right code into the 18M2.
It may well be that you can run some different displays with the AXE033 driver board, but my guess would be that you are limited to LCDs that have the same characteristics as the AXE033 LCD.
