Just as the title suggest. How difficult is it to destroy a level 8 portal compared to a level 7?
The "difficulty" of a portal is rarely a matter of pure portal level.
You can easily simulate an attack on this site, always keeping in mind that the results you'll get there are based on the observations of the agents on the field, since we're not getting direct informations from Niantic.
In terms of raw power, a L8 portal has only 8k hit points more than a L7 portal. A L8 agent usually will only need an additional L8 XMP burster to destroy the hardest portal.
BUT there are many factors that can complicate this scenario. First of all, portal Mods can make even a L1 portal hard to take. At the moment (patch 1.26) a L1 portal fully decked with the highest mitigation shields(+30) can sustain various hits from L8 XMP bursters without having a single resonator destroyed, more so if the owner of the portal is quick to answer to the attack notifications and recharges the resonators. Also, with patch 1.28, there's going to be a whole new set of portal Mods that will surely complicate the matter even more.
Also, every link on your portal makes it more resistant, so a heavily linked L7 portal may be harder to capture than a L8 portal with no links.
Once you factor in the actual position of the portals too, things get even more complicated. A L5 portal with a single L8 resonator placed inside a building can be an almost impossible - or extremely expensive - target, especially for low-level agents.
So, to recap: an unguarded, unshielded L8 portal in the middle of the road is only slightly more difficult than a L7 with a similar setup. Rarely you'll be in this situation though. L8 and L7 portals are the most prized possessions of both factions; they'll usually be heavily shielded, acting as nodes of many fields and with agents ready to recharge them at the first hint of an attack. In a real life situation I'd put them roughly on the same difficulty. Just remember that it's easier to deal with this kind of portals in a group: with each patch it's getting increasingly harder to take on higher level portals on your own, so always keep in contact with your zone's agents. Nothing can withstand the power of a group of well-prepared agents!
ADDENDUM POST-1.28.1: as foretold, patch 1.28.1 brought 5 new portal Mods. Of these only two are increasing the difficulty of an attack: the Force Amp and the Turret. Without getting too technical, they respectively increase the strength and the frequency/number of attacks. On the bright side, one of these Mods means that the portal will have less shields, but on the bad side this means that your XM reserve will last a lot shorter than before. Always remember to be careful and to pack up a lot of Power Cubes!
ADDENDUM POST-1.51: this patch unlocked the possibility to hack Ultra Strikes for every agent (previously it was limited to those with Motorola DROID devices). An Ultra Strike is a very high power attack item with an extremely narrow attack range. To use them effectively you have to physically stand on your target. Previously they could only be used to damage resonators, but the new patch introduced also a very high chance to destroy mods if fired directly on the center of the portal. This opens a whole lot of new strategies, with US used to remove mods and resonators being dispatched by the normal XMPs.