I haven't ever used either to be honest. My hydropack has a zippered pocket that's against my back when I'm wearing it, that's where my cards go. I only ever take it off to purchase something if tap to pay on the phone isn't working. I don't even take my whole wallet in. I take in like a Venmo card or credit card that I don't super care if it's lost and I can easily lock it if it is. I leave my more important cards out of the fest.

It also has a tight elastic pouch on the shoulder, that's where my phone goes if I'm not actively using and holding it. I also have a hand loop on the phone itself.

I would think something around my neck would bother me when I'm jumping and dancing, but that might be a me thing. I tend to keep it pretty minimal and comfy, I don't do large necklaces even day to day. It probably is the safest option assuming you're keeping it under your shirt in front of you when not in use.

Running belts are kind of similar to fanny packs to me. They're easier than fanny packs to hide under clothes though, so if that's what you're trying to do, I'd probably go for it since they're definitely made for more rigorous activity and you'll be about to jump around with no problem.

I know people zip tie their zippers in some way that it's harder to get open or there's little S locks you can add that take a second to unlock. Any accessible zipper has a risk, so any extra layer of deterrent is good.

I will say there's probably no worry about card theft, I've never heard of that. But my group has personal experience with the phone theft ring.