I checked out Consumer Cellular's site and they have a Moto G listed and below are the network technology specs, below that are the AT&T Samsung S4 specs.  The only key difference is on the Moto G you don't get LTE but CDMA and on S4 you get LTE and no CDMA.  So removing those two items, you will get GSM, Edge, HSDPA, HSDPA+ so you should be ok.
I pulled this data from here:
Moto G  
Motorola Moto G - Full phone specifications
NETWORK	Technology	
GSM / CDMA / HSPA / EVDO
2G bands	GSM 850 / 900 / 1800 / 1900
 	CDMA 800 / 1900 - CDMA version
3G bands	HSDPA 850 / 900 / 1900 / 2100
 	HSDPA 850 / 1700 / 1900 / 2100 - for T-Mobile, AT&T
 	CDMA2000 1xEV-DO - CDMA version
Speed	HSPA 21.1/5.76 Mbps
GPRS	Yes
EDGE	Yes
AT&T Galaxy S4 
Samsung I9505 Galaxy S4 - Full phone specifications
NETWORK	Technology	
GSM / HSPA / LTE
2G bands	GSM 850 / 900 / 1800 / 1900 - all versions
3G bands	HSDPA 850 / 900 / 1900 / 2100
 	HSDPA 850 / 1900 / 2100 - SGH-i337
4G bands	LTE band 1(2100), 3(1800), 5(850), 7(2600), 8(900), 20(800)
 	LTE band 1(2100), 2(1900), 4(1700/2100), 5(850), 7(2600), 17(700) - SGH-i337
Speed	HSPA 42.2/5.76 Mbps, LTE Cat3 100/50 Mbps
GPRS	Yes
EDGE	Yes