Wild Shape is not supposed to be on the same level of melee damage output as a fighter, barbarian or paladin - just like a paladin is not supposed to be on the same level as a spellcaster as a cleric or druid.
But let us take a look at statistics and numbers to see how Bear fares against a fighter like Lae'zel.
(I WILL BE USING DATA FROM THE FEXTRALIFE WIKI AS I HAVEN'T BOUGHT BG3. SHOULD THERE BE ANY STATISTICAL ERRORS PLEASE TELL ME SO I CAN ADJUST THESE CALCULATIONS)
At LVL 2 our Moon Druid in Bear form has 30 HP / AC 12 / +6 to hit / 2d4+4 damage
At LVL 2 Lae'zel has 20 HP / AC 16 (18) / +5 to hit / 2d6+3 (1d8+3) damage (Numbers in () are if she uses a shield and 1-handed weapon)
As we can see, those stats are pretty close to each other. The 10 point difference in HP is mitigated by the 4 point difference in armor class (assuming no heavy armor or shield, which Lae'zel as a fighter could equip). Even the damage output is comparable, with our druid doing 6-12 damage (average 9) and Lae'zel doing 5-15 (average 10) with her greatsword. Also our druid hits 5% more often. Yay!
HOWEVER! Moon Druids can wildshape as a bonus action, and you have 2 uses of Wild Shape, meaning that even if enemies manage to deal 30 points of damage to you, you can wildshape again to have ANOTHER 30 points of HP that they need to hack through - so in reality you have 60 HP compared to Lae'zels 20.
At LVL 3 our Moon Druid in Bear form has 30 HP / AC 12 (16) / +6 to hit / 2d4+4 damage (Number in () is if we use Barkskin)
At LVL 3 Lae'zel has 28 HP / AC 16 (18) / +5 to hit / 2d6+3 (1d8+3) damage (Numbers in () are if she uses a shield and 1-handed weapon)
At LVL 4 our Moon Druid in Bear form has 30 HP / AC 12 (16) / +6 to hit / 2d4+4 damage (Number in () is if we use Barkskin)
At LVL 4 Lae'zel has 36 HP / AC 17 (19) / +6 to hit / 2d6+4 (1d8+4) damage (Numbers in () are if she uses a shield and 1-handed weapon/ LVL 4 +1STR/+1DEX)
At level 3 bear druid might just be better then Lae'zel wielding a two-handed weapon because we have more HP, equal AC, better to-hit and equal-ish damage. At level 4 Lae'zel surges ahead because no matter if you take a feat or an ability score increase it will matter in combat, while druid wildshapes don't benefit from either. (Feats working or not in Wild Shape is a BIG point of contention in pen&paper circles. There are arguments both for and against it. I have no idea how it is handled ingame - if someone who has purchased the EA could provide clarification I would be very grateful.)
Also take into account that the above examples of Lae'zel don't account for your choice of subclass and fighting style - both of which can have an impact on those numbers (+1 AC / +2 damage with 1-handed weapons / Battlemaster manouvers etc.).
At level 5 fighters like Lae'zel get Extra Attack which catapults them ahead in terms of damage output. They now also have comparable HP to a Bear druid using 2 Wild Shapes. Add higher AC to the mix if you manage to find Plate Armor (AC 18 or 20 with a Shield) and its a fighters level to shine.
WHICH IS OK!! All this time while we have been comparing the melee capabilities of our Fighter and Druid pair our Druid has been growing in his capabilities as a spellcaster too!! It is this versatility, this blend of being a decent secondary melee character coupled with being a versatile full spellcaster when needed that has made Circle of the Moon Druid one of the strongest classes in D&D 5E for the past 8 years! We are a melee tank, melee damage dealer, battlefield controller, buffer AND healer!! ALL ROLLED INTO ONE SINGLE CLASS!!!
We should also not forget that, just as fighter-type classes got a big boost at LVL 5 because of Extra Attack, Moon Druids will get a big boost at LVL 6 because they will gain access to new Wild Shape forms. And seeing as we have not yet seen what Larian is planning to implement for those .... even if we don't get something with Extra Attack, as long as it's something that is an improvement to our earlier levels it's gonna be OK.
