Is military grade jet fuel more expensive than civilian grade?
Prices

Relative prices depend on what military fuel you compare to what civilian fuel. The current US Defense Logistics Agency pricing for jet fuels is as follows:

    Fuel type     $/gallon $/barrel
    JP8 &amp; JA1     2.15     90.30
    JAA           2.13     89.46
    JP5           2.18     91.56



JA1 is "Jet A1"--normal, internationally available civilian jet fuel. 
JAA is "Jet A with Additives". It's Jet A (which is slightly less expensive than Jet A1, but available primarily in the US) with some additives added to improve lubrication, reduce corrosion, icing, etc.
JP8 is the jet fuel the US military used for years before (semi-recently) switching to mostly using civilian grades. Basically Jet A1 plus some additives.
JP5 is used primarily aboard aircraft carriers. It has slightly higher density than the others, and a substantially higher flash point (>= 60C, vs. >= 47C for Jet A1/JP8).


Summary

The military designations are mostly slightly more expensive than their purely civilian-grade counterparts. The prices given above are also somewhat higher than the IATA shows for pricing on jet fuels in the general market, at least at this moment1.

Why

Part of the reason for moving to civilian fuels is to reduce costs. Along with that, using something that's widely used and available makes it much easier to manage the supply chain, ensure an adequate supply, etc.

References


Defense Logistics Agency FY 2018 Fuel Prices
JP-8 and other Military Fuels (Warning: PDF)
IATA Jet Fuel Price Monitor





1. At least as I read things, the price given by the DLA is intended to be used for budget estimates, so it presumably reflects their worst-case estimate of the average price during the coming year.