Okay, try this.
Say one aircraft climbs at 600 kt and can produce a thrust of 10000 lb at that speed. Another aircraft (same weight) can produce 20000 lb but only at 100 kt.
So with twice the thrust the slower aircraft can climb at a steeper angle-- but the faster one is moving so much faster along its shallower angle that it gains altitude faster. Power is defined as force times speed, and in this case the fast aircraft has thrice the power of the slow one. So it gains altitude faster.