Can different levels of the Church hierarchy provide different types of blessings? According to this question, In Catholicism, what does it mean for a priest to bless an object or person?, there is a "special apostolic blessing" that the Pope can provide. Blessings can also be provided by the priest.

Is there a hierarchy of blessings?

What is the difference, if any, between the blessings?
The Pope can bless objects and people implicitly during his audiences - any prayer and speech of the Pope gives Apostolic or Papal blessing to those listening and seeing the pope and to their loved ones unable to participate but connected through prayer. Any "holy symbol" the blessed people have with intention to have it blessed is blessed too (I guess that this doesn't apply to the loved ones who are not present, but I'm not sure). This is sort of a special rule, mostly designed to save time during audiences, when everyone wants to have something blessed.

And now let's return tu the "hierarchy of blessings": something like this is coined in Canon Law, canon 1169:


  §1 Consecrations and dedications can be validly carried out by those
  who are invested with the episcopal character, and by priests who are
  permitted to do so by law or by legitimate grant.
  
  §2 Any priest can impart blessings, except for those reserved to the
  Roman Pontiff or to Bishops.
  
  §3 A deacon can impart only those blessings which are expressly
  permitted to him by law.


There are blessings (as sacramentals; anyone can pray for blessing, but it's not this kind of blessing - see an answer for a related question for differences between priestly and lay blessings) reserved to the Pope, to bishops, to priests and to deacons - their hierarchy roughly copies hierarchy of Holy Orders or priestly ordination. I don't know if they are meant to be "stronger" and "weaker" - I think it's more a matter of personal faith and "collectors' sport" and in fact all the blessing are of equivalent "strength", but I might be wrong in this assumption.