I have to say I find the Orthodox description easier on the mind, and have difficulty with a hard and clear definition that one really can't prove.
I guess I still struggle with it, because if it is a miracle as stated - it's the only miracle God ever did that was not physically verifiable that I know of. The whole point of miracles is to show something. This seems to actually be supported by Pope Gelasius in the 400's. I did see a site that tried to interpolate his thoughts into transubstantiation - but I don't think it's right to do if taken as written.
Any thoughts welcome, as I can't seem to get around this, and I find myself still working on it.
In all reality, Orthodox and Catholics have the exact same belief and understanding of the Eucharist. When the simple bread and wine is consecrated it BECOMES the Body and Blood of Christ (substance), and yet we still only see, smell, taste and touch the properties of bread and wine (accidents), they don't change. It really is that simple.
Orthodox for whatever reason, not fully taking time to understand what we mean by transubstantiation seem to want to think we are talking about how this miracle happens. How this miracle happens, is outlined in the Mass, which is by the power of the Holy Spirit. That is the how, and I would imagine Orthodox would agree with this. The term transubstantiation only refers to what happens: After consecration the Host is truly the Body and Blood of Jesus, although we still see just bread and wine.
Now the council of Trent did define what happens and what does not happen session 13. The first three canons read:
CANON I.-If any one denieth, that, in the sacrament of the most holy Eucharist, are contained truly, really, and substantially, the body and blood together with the soul and divinity of our Lord Jesus Christ, and consequently the whole Christ; but saith that He is only therein as in a sign, or in figure, or virtue; let him be anathema.
CANON II.-If any one saith, that, in the sacred and holy sacrament of the Eucharist, the substance of the bread and wine remains conjointly with the body and blood of our Lord Jesus Christ, and denieth that wonderful and singular conversion of the whole substance of the bread into the Body, and of the whole substance of the wine into the Blood-the species Only of the bread and wine remaining-which conversion indeed the Catholic Church most aptly calls Transubstantiation; let him be anathema.
CANON III.-If any one denieth, that, in the venerable sacrament of the Eucharist, the whole Christ is contained under each species, and under every part of each species, when separated; let him be anathema.
This is the full teaching of the Church on the matter.