You can take out battledress with a RAM grenade.
It should be noted that the most common source of battlefield casualties are artillery fragments, not bullets. Stopping fragments is the primary purpose of military body armor. I suspect that this will be true in the future as well. This would imply that battledress is designed primarily to stop the far more lethal artillery of the future.
This is supported by the weapon statistics:
1. Combat Armor is first available at TL12 in CT. At that time, the Gauss Rifle replaces the TL10 ACR.
2. Here are the chances of scoring at least one hit at medium range (assuming +1 for weapon skill and taking into account the multiple hits rules in CT and Striker):
ACR DS Single Shot - 3%
ACR DS Burst - 66%
Gauss Rifle Single Shot - 28%
Gauss Rifle Burst - 97%
Unarmored troops would be hit 100% of the time.
In AHL/Striker, the numbers are more complex. The percentages are for Light Wound (3d6 CT damage) and Serious Wound (6d6 CT damage). Note that the burst percentages take into account the autofire multiple hits rule from Striker. Percentages in brackets do not account for multiple hits, which would be consistent with AHL.
Single Shot - 34% 5%
ACR Burst - 63% 15% [72% 7%]
Gauss Single Shot - 42% 10%
Gauss Burst - 49% 36% [51% 15%]
Unarmored Troops will be hit and suffer at least a serious wound 58% of the time with single shots; 83% of the time with an ACR burst; and 92% of the time with a gauss rifle burst.
Although the two systems have significant differences, they both portray battledress as being very vulnerable to the standard small arms of TL10-12, especially if autofired.
In CT, targets in battledress will be hit by HE grenade fragments 17% of the time. Unarmored figures will be hit 92% of the time.
In Striker, targets in battledress are basically immune from fragmentation. Unarmored targets will get hit 42% of the time. If hit, they will suffer a light wound 28% of the time, and a serious wound 72% of the time.
So battledress is useful, but standard infantry weapons of TL10+ can hit it. I'd expect that insurgencies would place a premium on acquiring TL10+ weaponry.
Single RAM HE and HEAP grenades are also effective -- in CT, they will hit (and almost certainly kill, wth 8d damage) targets in battledress 73% and 82% of the time, respectively. Plus, the aforementioned fragmentation. In Striker, they'll hit (and kill) a target 58% of the time.