They are basically the same, haxchi is cfw itself, it allows for loading unsigned content like homebrew channel, or any installed games by brazil method. Mocha is just used instead if you don't have haxchi, they both do the same stuff. One requires a paid NDS game and the other is free by web browser exploit which has less than 100% success rate, compared to haxchi. Once again, mocha is the poverty version cfw.
But you do need haxchi for coldboot i assume, i don't use cold boot cause i rather not deal with the long process of dumping a 32GB nand into a 64GB or higher sd card and if anything happens to sd card have to do it all over again, just be careful like me. Install from trusted sources and maybe install to usb storage first, at least is won't harm nand storage at all.