Much ink has been spilled over the concept of Anglican patrimony, but some of the candidates are more dubious than others. Is the reintroduction of traditional Latinate ceremonial (and I of all people mean that in no wise pejoratively) really a gift of Anglicanism to the church catholic? The Use of Sarum has been mentioned by some: others may dismiss it at as antiquarianism, but its recovery seems to have been relatively unproblematic in the Orthodox Church. (I continue to regard the Orthodox Western Rite as a more attractive options for Anglicans with swimming fever, though for various reasons I am not on the market myself. Nevertheless, TAC and its co-petitioners have won the goal of several generations of Anglo-Papalists and their integrity and readiness in "answering the call can only be commended).
Having said that, there are, I think, differences we can observe in the piety of Anglican Catholics and their counterparts in communion with Rome. Although I at first swam the Thames with Henrician intentions of remaining unchanged doctrinally and in practice, diligently praying the rosary and making periodic trips to the confession rail (boxes being nowhere to be found), there are certain things one does not generally find either in Anglican or in Roman Catholic churches.
Any kind of public Office is scarce as hen's teeth in the Roman Catholicism, although the Toronto Oratory offers the archdiocese's only Sunday Vespers (solemn, in the ordinary form, mostly in Latin, and with Benediction). There I notice that worshippers wandered in and out relatively casually - not irreverently, but clearly feeling no obligation to remain in a pew from ten minutes prior the service to the postlude or extinguishing of candles. Indeed, I have childhood memories of trips to the bathroom during the homily - you couldn't get there without passing the tabernacle and so you learned to genuflect with minimum pressure on the bladder.
Although there is the odd rosary group and Mass of the Sacred Heart, and Benediction remains a crowd-pleaser, the plethora of devotional options simply does not exist to the same extent in Anglicanism. It occurs to me that I don't know off hand where my brown scapular and Miraculous Medal are which I once doffed only to shower. Certainly the menu of Divine Mercy chaplets, perpetual Adoration, and Novenas to the Infant of Prague is not a feature of Anglican churches.
Roman Catholic churches often lack a cogent sense of community outside of worship. While many Anglicans cannot conceive of a Mass not followed by the eighth sacrament, coffee, in the church of my childhood "Coffee Sunday" was a once a month affair, and only if you happened to attend the 11am Mass after catechism instead of the 9am prior to, as most families with young children preferred. (As a teenager, I came to be partial to the Mass of anticipation and sleeping in on Sunday mornings). I certainly did not speak to other parishioners outside of the nave on regular basis. They can have a certain warehouse feel: friends tell of Masses being discontinued for attracting "only" 150 or so week by week - for Anglicans, an impressive figure for all Sunday services combined. Even outside of Anglo-Catholicism, Anglican congregations offer a "boutique" niche.
And so while communities of Anglicans received into full communion with the Holy See will be subject to the same doctrinal standards as other Roman Catholics, it seems fair to say that there are noticeable differences in the piety of Anglo-Catholicism that can be hoped to enrich the wider Roman communion in a real way.