More accurate for what?
I re-ask my original question: What do you forecast differently with a CAPE of 3,250 versus 3,000? Especially (in the real world) if you were to launch a rawinsonde in the same airmass at the same time 20 miles away, the CAPE might vary by 1000 j?
Mike, what do you forecast differently with an LI of -6.5 vs. -6? Both your question and my own are dealing with instability 'increases' of ~8%... But again, are you going to forecast differently for -6.5 than you would for -6?
I will agree that, because of the larger scale of CAPE (in the thousands) versus LI (in the single digits and occassionally double-digits), people tend to overanalyze model output (e.g. decide a target area based on ETA-forecast 2700 SBCAPE vs. 2500 SBCAPE), but from an objective standpoint, I certainly think that CAPE provides a 'better' view of potential instability. Yes, there's no way to eyeball it with much precision, so in that matter, LI is likely better if you are sitting out in a field looking at an 18z sounding. Then again, if you're out in a field looking at an 18z sounding, you obviously have access to a computer systme of some sort, and likely have access to CAPE calculations, as most sites put CAPE values on the sounding image.
Is it overused? Maybe... But instability is one of the key "ingredients" for deep convection... I tend to keep CAPE forecasts in mind when making a target area, since model forecast instability parameters are really all we have... I mean, you could just randomly pick a date and location sometime and hope for some action, but I'd rather take what we have (observations, model output, etc) and go from there... Yes, model forecasts of CAPE are sketchy, but again, that's the best we have. Until we have a surface observation network with very high spatial and temporal resolution (say, every 5-10 miles with obs every 5 minutes) nationwide, we have to make with what we have. Heck, one could argue that many convective forecast parameters (CAPE, helicity, bulk shear, etc) are meaningless given the high variability of said parameters, and given the paucity of the upper-air sounding network in the U.S. (and across the world for that matter), though that would make target-area forecasting success align more with luck than skill...