lvl 2 pidove (neutral/plus def), 0/0 IV
Tackle: (11)12-13(14) 1/16 to kill
Pidove catch rate: (89.076%)92.753-96.423(X)
Ember: 62.5% to OHKO
31/31 IV is the same 

lvl 4 pidove (neutral nature) 0/0 IV (18 HP)
Tackle: 10-11(12)
Pidove catch: 77.717-81.555

Ember: 12-13(15)
Pidove Catch (no burn): 81.555-85.353(92.753)
Burn does 2 damage
Pidove catch (burn): Guaranteed (timeloss to burn however)

lvl 4 Pidove (-Spdf nature) 0/0
Ember: 13-15(16)
Pidove catch: 85.353-92.753(92.753%)
Only max Roll + ember kills
Burn is Guaranteed 

lvl 4 Pidove (-def nature) 0/0
Tackle: 12-13(15)
Pidove catch: 81.555-85.353(92.753%)

lvl 4 neutral 31/31 (19 HP)
Ember: 10-12(13)
Pidove catch rate: 73.777-81.555(85.353)

Pidove needs 25+ IV in HP to have 19 instead of 18
Pidove needs 15+ IV in SpDef for rolls to change from 12-13(15) to 10-12(13)

Conclusion: Lvl 2 is objectively the best for catch ratio, while burn can help guarantee the catch (and wont kill unless max roll + burn if -SpDef nature), banking on a burn for the catch is not ideal.