That's a great question. It really all depends on the headphone. Anything that is harder to drive will benefit tremendously from the LC. Like HD800 with Mojo vs. HD800 w/LC + Mojo - there is no contest, it sounds 100X better with the LC in the mix. Same with hard-to-drive planars - mids be come fuller, bass more impactful, treble more controlled with the LC in the mix. But easier to drive headphones are sometimes better straight out of the Mojo because the benefit from the shorter signal path more than the additional amplification. It all comes down to the individual needs of the headphone.
All things being equal, the sauce comparison is a good one. The LC, will generally give you a fuller, more mid-centric sound than the Mojo alone. If you want that + more power + balanced mode, it is likely the best thing you're going to get until you get up into the $1,200-$1,500 range.
LC vs. Spark is another tough one that is not so cut and dry. If you ask people who have listened to both of them extensively, they are pretty divided on the topic. The LC benefits from balanced mode, more power, and a bit of a fuller/thicker sound. The Spark, on the other hand, benefits from battery power (and therefore no exposure to noisy AC power), portability and a sightly lighter more buoyant sound (without ever sounding whimpy. I mean it is POWERFUL). All things being equal (in terms of headphone demands), I prefer the Spark, personally (by a tiny hair), but it is 100% subjective. In
my writeup from RMAF 2015, I said it could be both "an endgame desktop AND portable for most Head-fi'ers " - I stand by that statement. That little amp is special.
