Perhaps some of the early versions had them but the current models don't. The AC-130H carries a couple 20mm Vulcans (up to 6000 rounds per minute), a 40 mm Bofors, and a 105 mm howitzer. The new AC-130U model dropped the two Vulcans in favor of a single 25 mm cannon. I'm not certain why they did that except it should be more effective against vehicles and armor. A 25 mm firing depleted uranium from fairly close range would do a number on the top of a tank. If that doesn't do the job, there's always the 40mm or the 105. The 25 mm appears to be the same gun used on the AV-8B Harrier II. It carries about 1800 rounds of ammo, enough to hit a lot of targets. Perhaps that's why they dropped the Vulcans, they went through so much ammo that it cut into time on target.

One big difference between the operational philosophy of the AC-47 and the AC-130 has to do with stealthiness. The AC-47s carried a lot of tracers so when they fired it looked like a firehose of bullets heading for the ground. Since the mission was to go after personnel, that made sense. The AC-130 loiters around an area for hours at a time, so reducing their detectability is important. One of the truisms of combat is that tracers work both ways. They're vulnerable in the daytime, as found out during the Gulf War. There was a heavy firefight and an AC-130 stuck around to continue supporting the ground troops even after daylight. It was shot down and all 13-14 crewmembers were killed.