In FS1, when you first start encountering the Shivans, there's less sense of hopelessness, and more of shock. As you start getting the targeting, better weapons, and shields, that shock starts to wear off, replaced by a sense that victory is now attainable. With capture of the Taranis, there's this feeling like you've turned a corner, and you'll soon be able to turn the tables and push the Shivans out. Then comes the Lucifer. From that point on, you can just feel the sense of hopelessness build, as the Shivans seem to be closing from all directions, with the unstoppable Lucifer leading the charge, showing up where no-one expects. The loss of the Galatea and the fall of Vasuda Prime starts the snowballing of that sense, as everything is in shambles and Command seems to be scrambling to form a pretense of a defensive strategy. Then, comes the Ancients find and a glimmer of hope, but with the clock ticking you get the real feeling of desperation, culminating in the final attack on the Lucifer on the final jump to Earth. Quite the epic.
In FS2, there's the brief feeling of apprehension. The last time the Shivans were encountered, they nearly exterminated the Human and Vasudan races, and the T-V Alliance managed to stop that threat by a finger-nail hold. This quickly dissipates after "Lion at the Gate", when the Shivans are dealt with fairly quickly by GTVA fighters and warships. After that, we're entering into Shivan space, so there's the feeling like we can do more than just hold them off, we can drive them back. There's still the concern about what size of fleet the Shivans may be able to deploy so Command keeps the options of closing the node or evacuating Capella and sealing off the nodes out. This is followed by an emotional roller coaster of "crap, what did we get ourselves into" and "whew... man, we really beat them off. I guess we got what it takes after all". Of course, once more Saths start to show up, its an obvious "OK, we're boned" attitude. This is tempered by the knowledge that Command plans to block the Shivan expansion, by sealing the nodes, so we're back to the "if we can just hold on a little longer" situation. Once the Bastion mission is successful, its a desperate race to get everyone out before the Shivans slaughter them all. Throughout that, is the fear of the unknown, as to what the Shivans are doing with the Capellean sun.