Hans,
when you say that you want to save pins. . . . . can you be more specific . . .
Do you already have an LDC dispay?
Are you already using it?
If so, how are you driving/writing to it? Parallel or Serial?
If say you have a PICAXE 18X and the LCD will be the only i2c device then the i2c will use 2 of the 8 available outputs.
By comparison, a serial interface only needs one output.
So if you are going to add other i2c devices like EEPROM, DS18B20 temp sensor, DS1397 real time clock etc later then the i2C comms method will ultimately save pins.
The AXE033 can include a RTC which needs i2C to read the time into the PICAXE. The AXE033 can also be written to for LCD purposes in serial comms mode.
If you already have a parallel type 2 line LCD display and dont want to buy another AND you have electronics assembly experience, then Revolution/PICAXE have an IC called the FRM010 which can be used to give a serial input to a 1 or 2 line LCD display.
The datasheet is not amongst the main collection of PICAXE datsheets but I have attached it here.
EDIT: okay saw you second post added while I was typing this. Rules out AXE033 but the FRM010 may still be useful