I see these as two pretty evenly matched teams. It's not really all that helpful to compare category by category to see if you have an edge, as it's not decathlon, where you see which team is better at each attribute.
That said, you both run press, and your starters are about equally talented on defense. You have a large shot blocking advantage, so that's a bit of a plus to you, but he didn't really try to score from areas where your shot blockers were, which works to negate that. In the end, each of your offenses has to face essentially the same defense.
On offense, you do have a lot more LP, so that's there to try to exploit... but that's not necessarily the best option. It's a lot harder score with LP than with PER, especially against a press defense. gillispie is right that you probably should have thrown up more threes with two very good to excellent outside shooters in your lineup.
gillispie is also right that fatigue is a killer. Slowdown would have been a better tempo option - you were at a substantial stamina disadvantage. Running slowdown, your starters would have stayed fresher and played more minutes.
For what it's worth, when it comes to evaluating your matchup, I'd take another look at my process if I were you. You had your team ahead in Speed, Athleticism, and Defense. Your starting five, overall, were actually slower than the opposition's five by about 20 points. Starters' ATH were within 10 points of each other. Starters' DEF were only four points apart. Four points is essentially a wash. You did have a rebounding advantage, but that didn't work out... partially due to stamina issues.
Again - I see these two teams being of similar quality, but I think oldresorter's team is slightly better, and would win about 55-60 out of 100 matchups on a neutral court.