Q:

How much protection do the various shields give

With the new levels of shields available as of 3 June 2013, is there an indication of how much protection each shield will give a portal?
Similarly, do they contribute to the XM drain on the attacker in any way?
For info on the new buffed shields, check out decodeingress:

Brandon Badger published on 31st of May that Portal Shields feel
stronger now. But there is a catch, only new obtained portal shields
are stronger. If you farmed those shields in last few months they have
same stats as old shields. Only new farmed shields have new stats:
Old shields:  Common +6
Rare +8
Very Rare +10
New shields: Common +10 Rare
+20 Very Rare +30

A:

As you assumed, new shields mitigations are :

common shield : 30
rare shield : 40
very rare shield : 60
AXA shield : 70

You can see those values in the app when upgrading shields.
Note that those values are for newly obtained shields, old one will still have old mitigation's values.
The mitigation of the shields is a percentage of absorption of damages. A (common) shield with a mitigation of 10 will absorb 10% of the damages made by the buster. A second (common) shield with mitigation 10 will catch 10% of the remaining damages.
For example, let's imagine a burster making 100 of damages on a resonator. First common shield will absorb 10% so damages will be reduced to 90. A second common shield will absorb 10% of the 90 damages and will reduce damages to 81...
In the worst/better case with 4 very rare shields mitigation 30, a burster making 100 damages will be reduced to 24.
To compute the total mitigation of shields on a portal you have to just multiply the percentages. A very rare shield will eat 30%, to compute the effects you'll have to do X - (X * 30 / 100) that will reduce to X * 0.7.
So a very rare shield is equal to a 0.7 factor applied on the burster's damage, a rare shield is equal to 0.8 and a common to 0.9.
So the way of computing damages is : 
RESULTING_DAMAGES = BURSTER_DAMAGES * SHIELD_1_FACTOR * SHIELD_2_FACTOR * SHIELD_3_FACTOR * SHIELD_4_FACTOR

And no matter the order of the shields, the result of a * is always the same :)

