TLDR: The only nickel-free strings on the market worth using. Get them if you suffer from a nickel allergy and hate the feel of stainless steel strings, or if you just want some great sounding strings, that will last a long time.
I have a nickel allergy that started out as an annoyance but ended up sucking all the joy out of playing guitar. I spent a lot of time and money replacing stuff on my guitars to make them nickel-free (even the frets!), but the one thing that caused me the most trouble was actually the strings. I tried all the alternative string-types: stainless steel, gold, cobalt and coated strings ...
Coated strings: They helped, but the nickel somehow got through the coating after a while.
Stainless steel: loved the sound, but hated the feel. They also ate my picks in no time and made a lot of noise when used with distortion.
Cobalt strings: Sounded great, felt a bit like stainless steel, but better - however, it turns out, that I, like a lot of people with nickel allergy, am also often allergic to cobalt.
Gold strings: Reminded me of a smoother feeling stainless steel string, but I just hated they sound.
When I was almost about to give up the guitar, I stumbled upon the D'Angelico Electrozinc strings and everything changed! These strings both sound and feel amazing! Don't let the D'Angelico Jazz/blues thing scare you off, I use them for everything from classic blues to hard-rock and modern metal. Just some really great allround strings - nickel allergy or not! Only complaint is the limited gauges to choose from, but I'm just happy that they exist.