just remember this:
you pull out the milspec armor, the GM pulls out the milspec commandos, Milspec mages, and the Milspec drones.
shoot first, shoot straight, and get the hell outta Dodge keeps you alive longer then "Me Tank, look at Me In Armor"....
Not at first. This is a trap far too many fall into. The whole "escalation" thing does not happen immediately, and it does not go straight to multiple Special Forces units with rocket launchers showing up to blow you up.
Yes, eventually bigger guns may very well be brought to bear, but security teams are not just going to "magically" turn into Mil-Spec commando squads with really big guns just because of one, two or even three times seeing someone using such gear--probably not even the fourth or fifth.
this depends on the "realism" of your gam e(and I use that term loosely in a Sci-fi/Fantasy game

)
Lets say you are using this armor on a run to a Corp facility located in the city (say a "B" zone like Tacoma and not in the heart of the Redmond Barrens where no one gives a crap

)
So you get in the front door, and the shit hits the fan... you have security coming for you!!!
well, the first wave of the security are going to be your typical goons... a couple of drones armed with heavy pistols and tazer type weaponary. The guards are going to be in armored jackets armed with heavy pistols and tazers... your typical "excuse me Sir, you don't belong here" force......
Until they round the corner and go "OMG! WTF??!?! HE'S IN MILSPEC ARMOR???" At this point, realism sets in (or SHOULD) No guard is going to try to go toe to toe with anyone in Mil spec armor when they are so vastly out gunned. the guards will retreat while screaming bloody murder into their links for back up and give an assessment of the situation.
For now, it's not a rolling gun battle, for a case of containment, herding and control. The building Rigger (assuming he's still up) will start to use the building against the mil spec guy by locking doors, dropping gates, and playing with the lighting. The spider might try throwing some drones at the Runner to tie him up and slow him down, and the security guards will do what they can with out readily endangering themselves.
All said, a SWAT level team is probably about 5 to 10 minutes away, and this will include a Mage or two who will probably send a spirit or two after the runner (the spirits can get there much quicker.... 1 to 2 minutes)
Now, even a SWAT level team as only a fair chance to take down a milspec armored foe, so they will try to use novel and unconventional tactics rather then your typical 'we line up like ducks to be shot' that most people seem to think

Overlapping fields of fire, flash bangs, drones, spirits, Mojo and the kitchen sink will be used.... anything that can throw off the Runner and not expose the SWAT team to deadly, lethal fire. Simply cause they too are only there to herd, and contain the Runner.
The REAL threat is the corp's own Military troops! now these bad boys generally are not sittingin a little room waiting to be called on, so they take time to get on site... say 30minutes to 90 minutes to mobilize and another 10 to get on site. And this is when the Runner is truly screwed!
But this is also the window that the Runner has to get the heck outta there, and A lot can happen in 40 minutes to two hours (like running out of ammo

) And then there is also the fact that the Corps are not above calling in the Police (that is what the police are for after all!) and the police are not going to just send a squad car or two, they are going to send what ever they can to contain the Runners to the Corp facility, cause after all, they don't want or need some heavily armed crazy running around the streets of the city!
Mil spec armor is serious bad news for Runners, it paints a huge neon sign on you and makes your life harder then you can know.