I think it’s a combination of personal preference and what you use it for.
If you need to frequently be amplified, investing in a pick up can save a lot of time & faffing with mic stands and positioning before each gig. You simply plug in and go. As someone who plays primarily rock and jazz, a pickup is absolutely essential; particularly when crammed on small stages with lots of band members. It’s less likely a pickup will amplify the noise from other instruments and takes up significantly less space.
You should also take into account whether you want to use effects; I realise I’m somewhat of an anomaly in doing so but attempting it with freestanding mics just won’t work very well.
However, if you are mainly playing solo and don’t mind taking a little more time setting up there’s nothing wrong with using free standing mics. Exact mic placement will vary depending on the acoustics of the room you’re performing in. In this way your can be more flexible than with a pickup. I feel two mics are needed to give a really big resonant sound but that’s not to say you can’t manage with just one. Assuming you’re playing places that already have a PA, it also means you have to carry around less gear. But if there’s no PA the opposite is true and good PAs are a lot more expensive than good amps.
I sing while I play so the mic set up just isn’t an option for me. My voice is always picked up by the microphone. However, I know plenty of people for whom a mic setup works great for, for things like solo wedding and church gigs. So it’s really just about finding what’s appropriate for you.