Thermostat Relay Positioning
Here's what you don't want to do.


  Try to haul 5 volts any appreciable distance. 


So I would lean seriously toward having the 24VAC wiring do the long haul.  

However, if you want the gory details, you need to examine each option: determine the current that will flow on the long haul, and grind that through a voltage drop calculator given the expected wire size and distance. 

The root of the problem is that a 0.5-volt drop only reduces 24V only 2%, but reduces 5 volts 10%.  Much worse, to do the same practical work, 5V needs five times the current, so 
now you're looking at 2% versus 50%.  In other words, voltage drop's practical burden is a function of voltage difference squared, so it is 25 times worse for 5V than 24V.