Regarding the first half of your question (why one might argue the Byzantine empire ended in 1204 rather than 1453), I'll just copy-paste my comment from the other thread:

That would be reference to the Fourth Crusade, which saw the Crusaders sack Constantinople. This also saw the Byzantine emperors removed from their own seat of power. This event came on the heels of a major decline in Byzantine power since the late 1100's as a result of the empire's terminal defeat in Anatolia at Myriokephalon in 1176, and the collapse of the empire's diplomatic power in the aftermath of the death of Manuel I Komnenos (Haldon, The Byzantine Wars, 201). Such an event was a critical blow to the prestige of the Byzantines, let alone their actual power and influence. Aside from losing their capital, their remaining territory in the Balkans was split up among several successor states. Constantinople was brought back under Byzantine control in 1261, but they never regained anything close to their former power and influence.

As for whether this date really marks the end of the empire, I'm sure that's just a point for debate. 1453 is as arbitrary a date for the fall of the Byzantine empire as 753 is for Rome, considering both these empires had seen their actual power decline to almost nothing far in advance of these dates. This is the problem with picking dates such as these to define sharp lines in historical periods where no such sharp lines exist, rather a gradual development of realities. I think it's fair to say that 1204 marked the end of the Byzantine empire's time as a major power, but I wouldn't say it is less accurate to pick 1453 as the final date for the end of the Byzantine 'empire', if it could be so characterised by that point.

I'm not engaged in the academia on the Byzantines, so I can't say what is the 'orthodox' view on when the empire "technically" ended, if there is one. If the wrangling around the date of AD 753 for the 'end' of the (Western) Roman empire is anything to go by however, to pick a single date for such major and gradually-developed events is perhaps more of a vague historiographical convenience than anything else. All you can say with 'scientific' certainty is that Constantinople, heart of the Byzantine empire, fell irreversibly to a foreign power in 1453. If you're asking in what year did the Byzantines terminally lose their status as a major power, then 1204 would be a more accurate date.

EDIT: By 753 I of course mean 476....