Generally the best option is simply to buy the given pedal if there is a certain effect you really want.
The Axe can do tons of stuff, and can do a similar sound, but its not going to be exact. I had a Game Changer for a bit, and found I just didn't use it enough to warrant the cost, for my needs. I just use a bit of reverb hold and it does the trick of what I'm after, but certainly isn't the same thing.
Same goes with things like the Digitech FreqOut! pedal. If, at some point the Axe can do it, then I'll gladly sell my Freqout, but until then, I'd rather have and enjoy something that does just what I want with the hardware pedal, instead of waiting on an effect setting which may never come.
If you want a "freeze" style effect, you can get pretty close. If you want exactly what the GameChanger offers, you need the real deal. Some great used prices too on these, which is how I got mine.