I would pick Lucario
As for typing in General, Lucario has better, with 8 resistances, two of them being 1/4, an immunity and three weaknesses.
As for Gyms, E4 and stats, the following applies.
Things Conkelder has STAB to(in Gyms E4 and Champ: Cheren, two of the Clay's, one of the Marlon's Pokemon, it doesn't have stab to any of the E4's, but does have super effective stab against Iris's Lapras, Aggron, and Hydriegon. It has better HP, Attack, and Defense. One of it's abilities raises it's attack when under extreme status, the other raises the power of moves with a secondary effect, but they lose that effect, which I don't think is worth it.
As for Defenses against Gyms and E4: It has a resistance to Wirlipede's Bug STAB, is resistant to Burg's Bug Stab, and Rock Stab, 1/2 resistant to Clay's Dark STAB, 1/2 resistant to Marlon's Rock Stab, resistant to Grimsley's Dark STAB, is Resistant to all of Iris's Dark and Rock STAB.
Things Lucario has STAB to(in Gyms E4 and Champ: Has all the stab advantage Conkeldurr, plus super effective stab to the Burgh's Dwebble, can do damage to Marlon's Jellcent, and all of Shantaul's Ghosts with Stab, and is super effective to Iris's Acheops, it has higher SP attack, SP Defense, and speed, as well as an ability that raises speed even more, if a Pokemon flinches, and has an ability to make it impossible to flinch.
As for Defenses against Gyms and E4: It has resistance to Cheren's Normal STAB, and is immune to Roxie's Poison STAB, as well as 1/4 resistance to Wirlipede's Bug STAB, is 1/4th resistant to Burg's Bug Stab, and Rock Stab, and 1/2 resistant to Burgh's Grass Stab, 1/2 resistant to Clay's Dark and Steel STAB, Same thing with Skyla's Steel STAB, 1/2 resistand to Drayden's Dragon STAB, and 1/4 resistant to Marlon's Rock Stab, resistant to Grimsley's Dark and Steel STAB, is Resistant to all of Iris's Stab except her Lapras's Water Stab, and Archeop's Flying STAB, it's and Aggron's Rock STAB are both 1/4 resistances.
So as you can see, Lucario has better resistance, they have equal amounts in stat's better than one another, and Lucario still has decent of the stats he's worse at than Conkeldurr, unlike Conkeldurr, who has terrible Speed, Sp Attack, and slightly worse, but still bad, SP Defense. Lucario has better Offensive STAB, and Lucario has better Abilities, as both of Conkeldur only work with a consequence.
Choose Lucario
PS: Whenever I just say resistant in this answer, assume 1/2 resistance.
Sources: Cross Referencing this and this, as well as this and this.
PPS: As an added bonus, another reason to use Lucario is it is easier to get, due to having to trade and train a Timber, into a Gurdurr, then trade it to get a Conkeldurr, while for Lucario, all you must do is have high friendship during daytime, which should be very easy, due to Riolu being extremely early ingame. First and only encounter is at Floccesy Ranch, at levels 5-7, which is really early.
PPS Source: https://pokemondb.net/location/unova-floccesy-ranch
