How accurate can you be in these circumstances about your own cadence, let alone someone elses? Granted, you may have some gadget that counts this, but it defies logic that two identically geared bikes were traveling at the same speed with the riders making different number of strokes per minute, if they were in the same gear. It isn't possible, assuming they have the same wheel diameter. Small diameter differences couldn't account for the cadence difference either you quote either (70 / 45) , so tyre pressure isn't the cause. Could it be that you just weren't well and it felt like you were pedalling slower and with more labour?

If that isn't it, then I'd check that the bikes are identically geared, and that yours is changing through the full range under load.

I think ZAC hits the issue above. Most likely your pal was in a different gear to you. I'd put it at 95% that this is the answer. You'd likely struggle to keep with him too if he was spinning as you say, because obviously he will exert more power with less exhaustion spinning than can be achieved by a similar rider working at a slower cadence.

Unless you looked at the block to check you were in the gear you think you were, there could have been some problem with your gear change. Maybe it stuck a gear or two higher, regardless of what you did with the shifter.