Will an ATmega2560 board be faster than a Uno for hard real-time data logging?
No, it will not be any faster. The extra instructions are to access the extra flash memory of the 2560. Instructions like EIJMP - Extended indirect jump, EICALL - Extended indirect call, etc.

The compiler option -O3 optimises the most, but there are other options you can enable, such as -funroll-loops which will cause major code bloat but speed things up.  Read the GCC manual pages to boggle at all the millions of optimisation options.

Or... use a faster chip, like an ARM or PIC32.