If you mean AuroraWright's yet-unnamed a9lh branch vs ShadowNAND.
They are basically the same thing, the only real difference is: AuroraWright's version uses the "arm9loaderhax.bin" or "arm9loaderhax_si.bin" to load external CFW's, whereas ShadowNAND moves that file to "homebrew/3ds/boot.bin"
Ultimately both versions of A9LH do the same thing. They both store a mini-CFW to the NAND and both have the same patches. They just both store their external CFW's in different places.
I personally use ShadowNAND because I like to keep my root clean of random files and keep my programs stored in folders.
If you mean A9LH (non-mini-CFW version) vs ShadowNAND.
A9LH can only boot from an SD card. ShadowNAND installs a min-CFW, so it can boot without an SD card or external CFW.
I honestly prefer the Mini-CFW. It feels safer to have another layer of protection for my A9LH install.