3 of 5 added 548 characters in body

I think this would be a more efficient way of doing it (at least for the printable ASCII characters):

++++[->++++++++<]                        Use cell 0 for loop and cell 1 for ASCII codes
++++[->>++++++++<<]>>>                   Use cell 2 for the space
+++>++>                                  Use cells 3 and 4 for the number equivalent
++++++++<<<<<                            Use cell 5 for incrementing the number equivalent
++++++++++++++++++++++++++++++++++++++++
++++++++++++++++++++++++++++++++++++++++ Get 95 for the loop
+++++++++++++++
[>.+>.>.>.+>-[----------<<->>>]<++++++++++<<+ Output ASCII & space & equivalent ASCII code
<<<]                                      Go back to cell 0

Tell me how this works for you... I don't exactly see why you need that comparing function. Also, note that I do use cell 6, but only to escape loops (as it has a value of 0).

Here is some different code with the same original formatting as the one in your question:

++++++++[>+++++++>++++>+>++++[>++++++++<-]>>>>>++++++>+++++++>>>>++++++>+++++++>>>>++++++>+++++++<<<<<<<<<<<<<<<<<<<<-]>++>>++>>>>>>>++>>>>>++>>>>>++<<<<<<<<<<<<<<<<<<<<>>>>>>+[->>>.>>>>>.>>>>>.<<<<<<<<<<<<<<<<<<.>.>>.<.>>>>>>>>>>>>>>>>+[->->>>+<<<<]>>+<[>-]>[>]>[<<<+<+>>>>-]<<<<>>[<<----------<<<<<+>>>>>>>-]<<<<<<<[->->>>+<<<<]>>+<[>-]>[>]>[<<<+<+>>>>-]<<<<>>[<<----------<<<<<+>>>>>>>-]<<<<<<<<<<<<+[->->>>+<<<<]>>+<[>-]>[>]>[<<<+<+>>>>-]<<<<>>[>+<-]+>[<->-]<]