Yes, especially the fact that you start with a rifle (BD) or an auto-sniper (PB) flattens power progression.
Activity of engagements are a mixed bag. On one hand, they have incentives to make you more active, like fatalities with berserker pack restoring some health, advanced melee and movement capabilities, or enemies throwing grenades. PB also turns hitscan attacks into very fast projectiles, which helps you be more active, however the fact other enemy projectiles are more varied in speed in PB makes dodging them less feasible and using cover more desirable.
What do you mean by "sandboxy"?
This is obviously not true. It's not surface level stuff that makes BD/PB good, the depths stays similar, just different.