One of the Battleships was destroyed and another one badly damaged when they detonated a Metreon cloud which the E-E released in front of them. The explosion is something of an oddity - the cloud appeared to be a massive chemical explosion, but even ignoring the problems with having such an explosion in space, you wouldn't expect a simple chemical explosion to be powerful enough to overwhelm a Starships shields.

However, the fact that this stuff is Metreon gas does offer up an interesting possibility. Voyagers episode "Jetrel" featured a "Metreon Cascade". This weapon was not really explained in any detail, but it did destroy most of the surface of an inhabited moon called Rhinax. The technobabble in the episode indicates that something other than - or as well as - a simple explosion was going on. Although it isn't really clear just how the Cascade did what it did, most of the victims seem to have been vaporized or disintegrated somehow - the episode featured Voyager attempting to reintegrate one of the victims using a transporter. So perhaps the Son'a weapon set off some form of the Metreon Cascade, which could account for how powerful the explosion seemed to be.

Alternately, or perhaps additionally, since both battleships were called in as reinforcements during the film then I suspect that they were also not fitted out for life in the Briar Patch. The Enterprise suffered damage to its Impulse manifolds when it pushed its engines in the Patch. If you watch the explosion of the first battleship on a frame by frame basis you find that when the blast hit it, its engines blew out before the rest of the ship. I wonder if the Son'a ships had damaged their own engines chasing the Enterprise, which could account for some of the first vessels susceptibility.

The second ship was badly damaged when debris from the first hit it, and I was tempted to make Son'a hulls very weak because of this. But that didn't really feel right - the Son'a are supposed to be at least as advanced as the Federation, since they are the only ones who know how to collect up the magic particles from the planets rings. The likes of Structural Integrity Fields - from which the hull of a Starship gets much of its strength - and armour are not especially advanced technology. The word "Battleship" (used in production drawings but not in the film) also implies fairly heavy armour protection. In the event I decided to make them somewhat weaker than Federation hulls, but still fairly strong - my assumption is that either the explosion or the battle with the E-E had previously damaged the ship, making it vulnerable to the impacts.