The 2EX V2s actually have wider dispersion than the LXs. The LXs have a larger vertical window, though (less important unless you are up and walking around a lot).
The LXs do put out significantly more bass and offer higher power handling. The 2EX V2s are a little more textured and "airy" in the top end, due in no small part to the wider dispersion of the ribbons. I own both, albeit in very different setups.
Subjective impressions warning: The V2 upgrade to the 2EXs provided a significant gain in midrange / lower treble fidelity and "spaciousness" to my ears. I generally find there to be a certain upper midrange leanness in most 2-way speakers, and the V2 went a long way in remedying this to my ears. I think outside of bass and sheer power handling I prefer it to the LX for this reason alone. Lacking a sub though, I'd go LX.
I also use a pair KH 150s (the bigger brother to the KH 120 IIs) on my desktop - again, in another very different setup to the others, so valid comparisons are difficult. These speakers are amazing and out-extend and out-SPL even the LXs. They also perform the "2-way that sounds like a 3-way" magic trick even better than the 2EX V2s do. They are narrower in dispersion, though, so at further distances this may or may not be a positive depending on your room and personal tastes.
Ultimately, any of these will sound great. They are all SOTA speakers carefully designed for a neutral response and good directivity (can easily be EQ'd).