There are two types of anti-static bag: static-dissipative (pink, red, or occasionally black) and static-discharge (silver or grey).
Static-dissipative bags are designed to remove any static build-up that gradually builds up during shipping by transferring the charge to ground (i.e. what-ever the bag is touching). However, they are not designed to handle electrostatic discharge (e.g. sparks) since they are not good conductors of electricity. Measured with a multimeter one should be able to measure a resistance through this material; I measured about 10M Ω across 1 mm. I don't have one at hand to examine but I suspect that the cross-hatched bags1 fall into this category. The red/pink bags use tallow amine as the dissipative additive while the black ones use carbon.
Conductive static-discharge bags, on the other hand, are designed to deal with sudden static discharges. They work by having a conductive metal layer (typically aluminum) usually beneath a thin, protective, often static-dissipative plastic layer. They protect the parts inside from sudden sparks by passing the current to ground (whatever the bag is touching) through the bag (and thus not the components within) with very little resistance; I measured <0.1 Ω/mm.
A third anti-static device that you may encounter is anti-static foam. This is a black, spongy, rough, and fairly firm material. This material contains a large amount of carbon and has a moderately high resistance; I measured ~100k Ω/mm. It prevents static build-up during shipment/storage at the component level. Static-sensitive devices are placed with their metal pins touching or piercing the foam (they are typically overwrapped with a bag as well). The foam ensures that all pins on a component are at the same electrical potential 2.
Dave Jones at EEVblog did a nice series of tests (YouTube) on various types of bags; well worth a watch. For preservation purposes the silver conductive bags would be the best choice. Since we're on the topic, static-sensitive devices should not be stored loose in polyethylene containers since they are very prone to building up a static charge.
1 Conjecture: I suspect that the carbon material can be printed on the bags while tallow amine needs to be mixed in to the plastic. Using a cross-hatch pattern would be a cost-saving measure.
2 One manufacturer I know ships their boards in bubble wrap envelopes that are silver on the outside and pink on the inside. In this case the outer layer protects against sudden discharges (i.e. sparks) while the mildly-conductive inner layer keeps all pins/traces on the enclosed board at the same electrical potential.