The thing that best illustrates the similarities and differences between batman and hal jordan's lantern is that quote that i can't find anymore about how batman has contingency plans to not fall off a cliff while hal figures it out on the way down. The best example of this is their plans to take down the justice league.
Everyone knows Batman's excruciatingly detailed plan on taking down the league basically almost before they become a real threat in an active fight, and the plan counteracts each league members specific strengths.
Hal also has a "plan" (in the loosest definition of the word because it isn't really a plan so much as hal going "hmmmm...if i were in this situation i would..."). the plan is from The Last Will and Testament of Hal Jordan and immediately the differences are obvious. hal's strategy begins once there is a fight to be had while bruce neutralized everyone before it could get to a fight. hal's plan is entirely dependent on what he knows about the league members as people like when he points out barry's habit of running faster than the problem and hal's idea is to trap him on a mobius strip construct or his insight into superman's fear and how he could use that against clark.
i'm not talking about which plan works better or anything, i'm talking about how their respective strategies show exactly who they are. bruce is pre-meditated, and meticulous and based on data and experience while hal's strategy is an on-the-fly situation, based on his personal interactions and observations.
Edit [thank you to @latovii] : The quote is 'Hal Jordan – he’s the anti-Batman. Batman has everything mapped out seven ways, while Hal will jump off a cliff and figure out how not to die on his way down.'