OK, I will bounce around a couple of ideas. I am sure some of the more seasoned captains and stokers will also chime in.
In the case of a male captain and female stoker, on single bikes, the male can out-climb the female most of the time. I will assume this is true for you two. In theory, you should be able to climb on the tandem at a pace somewhere between your pace and your captains if each of you were on single bikes.
I would offer that the bike has less to do with it than with dissimilarity in climbing styles. Do you like to sit and spin and he likes to sit and mash? Or, maybe he climbs grinding a huge gear while standing on a single?
It takes time to get in sink with each other.
I have captained with several different stokers. I would bet that if I was riding with the fittest of the stokers, we could climb with all but the fastest males, and this is on a low-end tandem. She and I liked the same cadence and were quickly in sink when standing.
So go out and ride more! Communicate! Work together!
PS…if you do get gapped on the climbs, just catch back on the flats/descents….