I happen to have both from BCM, a 16" LW middy and a 20" gov profile.
The 16" LW middy is accurate enough with M193 and irons (intent was not a bench gun) and the whole gun weighs 6.5lbs. The LW profile saves about 4 oz out front vs gov profile barrel. It heats up quick but that doesn't seem to affect it's groups, not nearly as severe as my 580 series Mini 14 (it's groups double in size when hot).
My 20" gov profile is setup similar to an M16 A2 (but with detach carry sight), and shoots just fine, weighs just over 7.5lbs. The bullets are really flying out of the 20" based on bullet drop. M193 shoots combat accurate (irons only), but considering it's LW under the handguards, an A1 profile barrel would've been better. But I got the complete 20" upper cheap when they were selling with free CH and BCG, so I wasn't too picky. I basically just wanted to put together a more traditional looking 20" with no real purpose for it in mind.
If you are doing run 'n gun, carrying it alot, or just want the best handling AR get the LW. If you want the most accurate bench gun or do lots of mag dumps, you want to look for a medium or heavy profile barrel; the gov profiles are still LW under the handguards but add unnecessary weight way out front. If you want a truly classic looking A1/A2 I would start with a dedicated retro upper.
Personally I prefer the 16" LW middy by a long shot.

