I would strongly recommend that [high side sensing], so you can maintain a solid ground plane under everything, improving signal quality and reducing EMI.
As for mV here and there, no, it doesn't really matter, except where it obviously does (e.g. ADC or other analog I/O, RF, etc.). In particular, digital logic (LVCMOS) doesn't care.
The details:
In principle, the admonition should really be that at least one supply remains tied to its plane. You could float local ground, so long as it's all bypassed to VCC as appropriate, and the VCC plane in turn covers much of the board. This is more acceptable when loads are largely VCC-oriented, i.e., active-high signals with loads sinking to GND. However, both device capability, and tradition, go against this -- CMOS pins pull down stronger than they pull up, so it's preferable to use active-low signals (loads sourcing from VCC), and so local grounding is more critical. This isn't to say you can't do otherwise, but you won't have as much capacity (total mA load?) or as good performance (e.g. saturation voltage, speed) doing it the other way, and that can make the difference in some applications.
Also, as it happens, most devices are specified with total equal supply current limits. So, unless you need the lower voltage drop, or lower total power dissipation -- you'll only be able to use up to the total capacity in a given polarity, and that's it. The consequence is, you have the most total capacity using a mix of both. That is, if you want to light up as many LEDs as possible from a single MCU, use a mix of active-high and active-low loads!
Tim