I’m a hiring manager, and no. I care about what you know and how well you can articulate that knowledge. There is probably some correlation between strength of candidate and pursuing a harder (?) degree, but it’s probably not that strong. I’ve hired people who didn’t even study CS at university for SWE.
BA vs BS doesn’t matter for a lot of companies, but it does for some and especially for some career trajectories. A BA is probably a non starter for data science, ai, ml, quant, etc type jobs. I believe the government also is picky about it. If you don’t mind either way and the only difference is calc 2, the BS is your best bet in terms of robustness. But it’s not a major deal either way if you just want general SWE jobs.