Deciding whether to help Songbird or Reed is really the crux of Cyberpunk 2077's new Phantom Liberty expansion, as you align yourself with either the escaped hacker or the grizzled ex-FIA agent. Both make pretty good cases for why you should pick them, explaining their respective plans during the Birds With Broken Wings quest.
Songbird wants to escape Hansen and find a way to cure her Blackwall infection, while Reed thinks Songbird needs to be captured for her own safety and the safety of others. Whichever choice you decide to make in the Firestarter mission has a massive impact over the rest of your time in Phantom Liberty, altering both your remaining quests and the ending you can choose.
While I won't spoil endings here, I'll lay out each option, its immediate consequences, and what kind of ending it'll open up for you. It's also worth noting that choosing either of these options will let you unlock the new ending for the main game. This guide will of course contain spoilers, so look away now if you don't want them.
Help Songbird escape
If you choose to help Songbird escape from Hansen and Reed during the Firestarter mission, the first immediate consequence is that Hansen dies. When Songbird says to give Alex the signal, she'll pull out a gun and murder everyone in the observation room above like planned, before realizing that you're doing a runner with Songbird.
Another immediate material consequence of this is that you won't fight Hansen yourself, and so won't be able to claim his three Iconic weapons: Fang (Knife), Bald Eagle (Power Revolver), and Wild Dog (Light Machine Gun). You will, however, be able to kill Murphy on your way out of the stadium and take his Iconic Murphy's Law (One-Handed Club) instead.
While each of the separate endings still has a choice you're required to make, helping Songbird escape ultimately leads to what I'd call the "good" ending. While I won't spoil the ending choice itself, in this version you find yourself infiltrating the Night City spaceport to help Songbird find a cure for the Blackwall infection that's killing her.
If you ultimately sympathise with Songbird and want to spend more time with her, get to know her better, and help her achieve her goal, you should absolutely pick this option.
Help Reed capture Songbird
If you decide to use the Icebreaker Reed gave you to capture Songbird instead, the first immediate consequence is that Alex dies instead of Hansen. When Songbird realises you're betraying her, she warns Hansen, who then kills Alex in the observation room. Songbird also tries to resist the Icebreaker by accessing the Blackwall, which causes her to go on a rampage through the stadium.
In this version, you fight Colonel Hansen as you escape, and so get to claim his three Iconic weapons. Reed comes to pick you up and you chase Songbird to find her being captured by MaxTac after she collapses post-rampage.
Again, you will still have a choice to make at the end, but this version of events is far darker, as you free Songbird from MaxTac and pursue her into a Militech bunker under Dogtown. If helping Songbird is the option that relates to her personal struggles, helping Reed is more about how accessing the Blackwall has changed her and the darkness she's struggling with.
If you don't trust Songbird and want to align with Reed, Myers, and the FIA, this is definitely the option you should choose.