In my opinion for fast and fun, magnets are great. Tie downs give more precision and control, but take longer to tie down. Like most things in stop-motion it depends on the outcome you want to achieve.
What if you used magnets and tie downs for one armature?
I haven't used magnets to hold down a wire armature, but I do use a wire armature with tie-downs. Here's what I think would be things to thing about: Wire armatures work well for light characters, but if your character is heavy, (like his head), then you'll need a really solid anchor for them.
Wire armatures can sag, can droop, and can bounce when you position them. That _might_ be made worse by using a magnet on the feet. It's one more point of failure/sagging. Only exploration and experiment will tell you how it works for you. give it a go and if they work, then go for it!
My wire armatures don't sag or droop, but they can be a bit bouncy! For lightweight puppets the magnets would work fine, but if the puppet is heavy or thick, like a silicone Sumo wrestler I made for a client, the armature needs to be fairly stiff to fight the thickness and weight. It takes a lot of effort to move it, and a couple of times I've actually lifted the set floor just animating the puppet. The tie down doesn't let go, no matter what, but I don't think a magnet would hold very well for that puppet.
With tie downs, my puppets can be animated falling down, attached by one foot, and even when the puppet is horizontal and an inch off the floor, it will hold its position. (Also requires the armature to be strong and not too loose.) You may not need that, but all puppets will be off balance to some degree in the middle of some moves - a walk is basically falling towards the leading foot until it hits the ground. A good magnet will cope with a normal walk. The ones I've seen (at McKinnon and Saunders) had steel in the foot, and the rare earth magnet under the set. That way the magnet can be bigger. (They were the size of a C size battery, and had a screw up the middle to help push them away from the floor until the magnet was far away enough to weaken its grip.) If the magnet is in the foot it is limited in size, and also as the foot gets close to the steel floor it will snap onto it, so you can't do a frame with the foot just barely above the ground.
There is a big advantage if you have smooth shiny floors where you can't hide any tie down holes, but I just avoid those kinds of floors and stick with tie downs.