Scientific fact isn't an opinion.
Nope, when in SERIES the performance will be determined by the weaker (higher resistance)
battery BUT when they are in PARALELL (like the OP will be connecting them) the resistances of the two batteries will parallel to form a new resistance that is lower than either of the original batteries, that's simply Ohms Law.
The two batteries effectively combine to form a single
new battery who's capacity will exactly equal the sum of the original two batteries, that's Kirchhoff's Current Law.
If the chemistry and cell number is the same then both batteries become 'flat' at the same voltage as each other and also become 'full' at the same voltage as each other.
Because they are connected in parallel they therefore become 'flat' and 'full' identically. It doesn't matter how old they are or who made them or what capacity they are. They both attain full capacity and full discharge simultaneously and therefore their relative capacities of both batteries are fully utilised.