I am a bit cynical on the topic of ULA. They have been running what I consider a scam for a long time, and because there was no competition, we saw what happens in a monopoly situation.
ULA has used the claim of reliability and payload size in the past. They have not had a failure of a payload in over a decade and over a hundred launches. Thus for unique and expensive payloads, the suggest that the extra cost is worth it for the record of success in the past.
For very large payloads, the Delta 4 Heavy and Atlas 5 551 are the heaviest launchers, and more powerful than a Falcon 9 1.2. This will remain true until the Falcon Heavy becomes operational and has a few flights under its belt.
The upper stage of a Falcon 9 is its weakest feature. It has a high thrust engine (almost 200,000 lbs of thrust), but not the greatest Isp (311s). Whereas ULA uses the Centaur upper stage on both Delta and Atlas launch vehicles. That uses one or two RL-10 engines, which while much lower thrust (25,000 lbs) has MUCH better Isp (450-465s) which makes a huge difference in an upper stage.
Secondarily the Falcon 9 upper stage cannot coast long periods and relight but a Centaur can. Thus GTO missions (Geo Sync Transfer orbit) where the payload does the extra work to get to GEO are possible, but Falcon cannot directly insert into GEO since it cannot coast and do the final burn the many hours later that is required.
People in the forums have run the numbers for a Falcon 9 with a more Centaur like upper stage and it gets much larger payload numbers.
For interplanetary missions, the Isp difference matters a great deal in terms of what can be lofted to various destinations. (Not getting into a discussion of C3 here).
ULA has played these two cards heavily in the past. For GPS III launches they did not even compete, since GPS III was basically an assembly line payload, and if one was lost, just build another one out of the insurance money. Based on price alone they had no chance so they did not bid.
Now that SpaceX has a history of 26 or more launches (Depending on when you read this) with only one well understood failure the reliability argument is going away. Some would argue that the re-usability and recover of the first stage will make them more reliable. That is, they have now seen what a stage looks like AFTER it launches and returns. This can only help refine the vehicle.
For special one off NRO missions, or maybe the James Webb Telescope, the reliability argument can be a powerful one.
Elon Musk has tweeted that he would love to redesign the upper stage of the Falcon 9 but needs to focus on Mars first. It is good enough for almost every payload they wish to win, so not important to fix right now.
When they have a working Raptor LOX/CH4 engine, then they may reconsider a smaller version for a Falcon 9 upper stage, since its improved Isp makes a big difference in performance.