Late to the party, but yes, trying to have a rigger and drones stack up against a mage and their spirits in combat is like trying to get a Face to stack up against a Street Sammy. So long as they aren't dead weight, and can at least defend themselves a little, you're already calling this a win. A man with either a couple armed and armored drones or a swarm of lightly-armed drones against a mage (with their magic) and spirits who can go through walls to attack people from behind, and are immune to normal weapons... there's no way you're going to make that fly without turning Riggers into gods or nerfing Mages to the point where they're worse than TMs.
So start off with the simple question of: What is a Rigger good for? Sounds snarky, but hear me out. List the things a rigger does well, and compare them to a mage and their spirits in that category.
Transport: One of the more overlooked areas for riggers, since everyone focuses on drones, but being able to get the team to and from the gig, sometimes passing through or avoiding security checkpoints, and often under fire, is no small thing. I mention this first because it is the one area where no mage even comes close.
Tech Support: More the hardware side of things, but a Rigger and their drones are able to interact with technology much more easily than spirits can. You need to get a tap on a line on the roof so the hacker can get access to the building's network? You got three options, really. Have an Infiltrator get up there somehow to plant the tap, have a spirit fly up there to plant the tap, or have a rigger get a drone to plant the tap. Of these, the only two that are any good at it would be the infiltrator and the rigger. The spirit can't hop planes holding the physical module to tap the line, and because they have trouble with tech in general, the mage would have to project and manifest with them to tell them what to do, assuming the mage has the knowledge necessary (big assumption). A rigger jumps into their drone, and plants the device just where it needs to be, because they know what they're doing.
Overwatch: Sure, a mage with their spirits can be invaluable at watching over a scene, but they are still babes in the woods compared to a Rigger who becomes the building, or has several drones disguised as advertisements (possibly even broadcasting real advertisements) watching over the situation. And when some of those drones are armed with sniper rifles... But even better than what you get with a spirit is that the Rigger can share tactical data in real time, without playing 'telephone' and interpreting what a spirit saw from what they said, and then telling it to the team. You can send an alert to everyone's HUD, letting them know what you're watching, or sharing footage so they can see for themselves, and plan accordingly.
Mobile Support: Going on with some of the earlier points, there are few better for providing mobile support than a rigger with a few drones loaded for bear. Since drones basically live or die by speed and maneuverability, keeping them moving is important, but something as simple as a Steel Lynx, driving alongside your van, turning to fire the underbarrel grenade launcher on the rifle you put on its rifle while you are trying to escape can do a lot, without exposing your team (who may or may not already be wounded) to return fire. Sure, a spirit COULD attack a vehicle in passing, but would they be able to launch a slick grenade to explode on a tight turn, sending vehicles into a crash? I think not. And if the mage is already beat up, he might not have it in him for an Ice Slick, or he'd be out for the rest of the run, when you might need him more, later on.
Kamikaze: Sending people or spirits on suicide attacks tends to make you massively unpopular. Drones, on the other hand, are relatively cheap, and can carry a payload somewhere that people will not appreciate it, with minimal risk to the group sending it. Especially nice for those times you have to play with WMD.
So that's what a rigger is GOOD at. Now let's talk combat. Because combat will happen.
DON'T: Get in a standing firefight. Sitting still for drones is a death sentence, like hovering in a helicopter when the other team has AAA weapons.
DO: Keep moving. Cover is your friend. And you have more recoil compensation as a drone than a person normally has as a metahuman. Use that. Cover to cover, with burst fire to reduce defense...
DON'T: Try to win combat by yourself. You will fail.
DO: Focus on how you can get your team an advantage. Covering fire while they try to get through a position, flanking a position to fire from a new angle, and so on.
DON'T: Go toe to toe with combat monsters. You will fail.
DO: Cheat. No defense test on attacks you're unaware of. Sniper rifles on drones are just as fun to deal with as snipers themselves.
A rigger in combat should focus on getting out of combat as fast as possible.