The principle aspect of Roman monastic praxis that is or at least appears counter to Orthodox approaches is the emphasis on ecstatic experiences and the imagination in prayer. On fatheralexander.org and orthodoxinfo.com, admittedly both traditionalist sites opposed to any attempt at reconciliation (IMO the attempt itself is worthwhile, but reconciliation should be on our terms), there exist comparisons of the lives of Abba Sisoes and Francis of Assisi that are highly informative.
Strictly speaking, the Franciscans are not a monastic order. When considering "Roman monastic praxis", I'm not sure I see anything incompatible with Orthodox monasticism. Liturgical prayer, work, fasting, silence, prayer of the heart, the spiritual father, etc. are all part of both forms of monasticism.
Also, can the Orthodox in Union with Rome really suffer the superstitious use of the miraculous medal and the scapulars?
How are you defining superstition?
...then you have traditionalists like the Rorate Caeli blog and Latin Mass priests starting up new Purgatorial Spcieties, already with thousands of souls "enrolled", and celebrating Requiem Masses on Nov 1 "for the poor forgotten souls" complete with black palls with frightening real human skulls and crossbones at the base (see Fr Zeds blog wdptrs), and this really seems unorthodox to me in the extreme. Yes we pray for the dead, even those in Hell based on St. Macarius, but the specifics of purgatory and spooky requiem masses (although with lovely music and black vestments) seem in opposition to our approach towards this vital form of prayer, vital in that it benefits the living as much as those awaiting resurrection.
Prayer for the departed, whether by name (when we have names) or without them, is also a part of our Orthodox tradition.
What's wrong with Requiem Masses?
Nothing is wrong with Requiem Masses, but the specific intent centering around Purgatory. I love Requeim Masses and at the same time regard Purgatory as a distortion of Patristic teachings regarding the state of the soul after death. So a requiem mass is fine, but a requiem mass whose sole purpose is to accomplish something specific regarding those in purgatory is a reflection of this Scholastic distortion of the Patristic view. Now granted, it might well help those who have died; I am a supporter of prayers for the dead, but I'm against purgatory.
Also, I love black vestments and am entirely untroubled by the Great Schema, unlike Mor, I was only a little creeped out when I first saw one, quickly got over it and grasped the meaning, and never thought it looked Satanic, but I don't fault Mor for thinking that about it as the Great Schema is definitely spooky looking. I first saw it on wikipedia when doing some reading years before I became Orthodox. What I do object to is the gratuitous and unnecessary display of human remains. Fr. Zed celebrated a requiem mass in which the pall used over the thing they place in lieu of the body at General Requiems featured a real human skull and crossbones in the Pirate Flag pattern, and not of a departed saint. This IMO is unacceptable and grotesque, just like the displaying of the embalmed but not incorrupt body of St. John XXIII for decades before his canonization in a glass coffin. He wasn't a saint and his embalmed body wasn't incorrupt, according to the church itself, so why display it? So the faithful can watch it rot, albeit very slowly?
The display of incorrupt or semi incorrupt relics on the other hand I do not object to, although in a few cases I'm not sold as to their incorruption (the blackened skin of St. John Maximovitch comes to mind, although a priest told me it turned black because on finding it incorrupt they washed the body in wine, so I take his word for it, although I do confess not entirely understanding the point of doing something to incorrupt remains that makes them look corrupt).
Now, regarding the miraculous medal and certain scapulars, some of them are worn with the idea that if you die wearing them, you will avoid purgatory (the brown scapular); I forget what the miraculous medal does, but these are generally based on Marian apparitions, and my chief criticism of Roman spirituality is that their discernment process for Marian apparitions is not sufficiently robust. It does exist, which is why Our Lady of Amsterdam and of Medjugorje have not been formally approved by the CDF (although the new Archbishop of Amsterdam unlike his predecessors is trying to reopen the case), but it does not seem sufficiently robust by Orthodox standards. I believe the late Bishop Alexander Mileant included on his website material specifically addressing this point and in particular Our Lady of Fatima. But what makes the brown scapular et cetera superstitious is the specific assurances that come with them, I.e. wear this and bypass Purgatory. Tjese objects become fetishes, their use justified on the flimsiest of evidence, apparitions of Jesus or Mary often to a single monastic or layman which would never be accepted in the Orthodox Church. And their use is incompatible with the Orthodox understanding of what happens to the soul after death, regardless of whether or not one believes in the Aerial Toll Houses, for instance. But let's say one does; why is it then that in Orthodoxy we lack any kind of equivalent scapular or medallion to allow us to bypass the toll houses? And furthermore, if these scapularrs have the effect that is claimed, and some Popes have believed in them, why not order them issued to all the laity gratis at baptism?
Now regarding Roman monasticism, the main difference centers around the striving for ecstatic experiences, apparitions and so on, the frequent occurrence of stigmata, and other visions (from which devotion to the Sacred Heart of Jesus and the Immaculate Heart of Mary is based), which have been allowed to influence the dogma of the church. The Philokalia specifically warns against this approach; it warns against the use of the visual imagination in prayer, which Catholics do when meditating on the mysteries associated with each decade of the Rosary, and it warns against seeking visions, because the devil will exploit this desire and provide false ones. Why was St. Francis the first person since (possibly) the Apostle Paul to be a stigmatic? Why didn't earlier saints like Ignatius, Justin Martyr, Athanasius, the Cappadocians, Anthony, Macarius, John Cassian, Augustine, Benedict, Scholastica, Columba, Gregory Dialogos, Columba, Isaac the Syrian, John Damascene or Patrick receive these marks? And correct me if I'm wrong, but why have no Orthodox, Eastern or Oriental, received them since? Yet Rome has since Francis produced a steady stream of stigmatics, most recently Padre Pio, who was accused of using ammonia to keep naturally caused wounds disinfected and unhealed, although the church rejected that claim and I am willing to accept it as having an unnatural explanation.
Now this is not to say everything in Catholic monasticism is bad. Certainly the basic pattern of Benedictine monasteries and their derivatives (Cistercian, Trappist), and Carmelite deserts, is identical to the Orthodox model, and the Carthusians are a bit like idiorythmic monks on Mount Athos, albeit with lay brothers to support them. This in the medieval times allowed Cathusian choir monks to focus on copying manuscripts, which was at the time vital and laborious work well suited to a monastic, and Carthusians also grow their own vegetables in their private gardens. I bitterly lament the great schism occurred just before the time of St. Bruno as I love the Carthusian model. I also admire St. Dominic, although not what is order did after his death in the Inquisition. But the Dominican insistence on Orthodoxy appeals to me; they have often acted as a restraining force on the excesses I described earlier and throughout much of the history of the church, especially in recent times, the Holy Office, or CDF as it is now known, has sounded like a voice of reason. But in perusing the history of the OP, setting aside the inquisition, one can still find a lot to object to, like Thomas Aquinas and his Summa Theologica, which defines Scholastic theology in the same way that John Damascene defines Patristic Orthodoxy (at least from a Chalcedonian perspective, but a local Coptic church uses a prayer written by him on a printed laminated card as a Post Communion prayer, and there's not a lot in his Exact Exposition that an OO would object to), and this work unfortunately became the main reference for Catholic theology.
So if reunion occurs, I feel as though a priority would be the reform of Roman monasticism chiefly by seeking to stamp out striving for visions, the veneration of stigmata, and so on, by requiring the Philokalia along with the Ladder of Divine Ascent to be the training manuals for every monk; in my opinion they are much more important than the Rule of St. Benedict (parts of which are out of date; the corporal punishment of monastics by their superior is completely unacceptable, if not utterly contemptible, in the context of contemporary monasticism).