The single difference that will have the most effect on an ongoing campaign or one shot adventures with characters above 3rd level is in Lamentations of the Flame Princess the only increases to to-hit bonus are received by the fighter. The fighter has a +1 bonus to-hit over the other classes at level one as well.
The result is a 10th level cleric, magic-user, elf, dwarf, specialist (read thief), or halfling fights as though they are first level and fight worse than a first level fighter. This has a huge effect when fighting monsters with very good ACs (2 or less in descending) that are common in higher level modules. If you use Lamentations of the Flame Princess you will probably want to adjust AC more than just the +/-2 difference it has from other OSR games or have a more fighter heavy party.
The second biggest difference is thiefs, called specialists in Lamentations of the Flame Princess. They will be superior to their LL counterparts for most skills at most levels but deficient in one (climbing). At first level their worst score will be 1/6 or 16.67% which exceed their open locks, find/remove traps, and hide in shadows abilities. They also have four pips to increase skills at first level with two more each level after. Thus, it is possible for a first level specialist to have a 5/6 chance (83.33%) of detecting a trap at first level even spreading equally will have two at 2/6 which exceeds LL in all but climb assuming they devote one pip to sneak attack.
Unless points are spent on sneak attack the specialist has none and while one point will double damage the attack bonus is only +2 not +4. Again, you'll need to look at a given module's assumption about thief skills and adjust accordingly.
The others differences listed also need to be taken into account but I consider the changes in to-hit and thief skils keys in running something designed for other TSR D&D influenced games.