Since there's no baroque throat there is no organological evidence of a different way of singing in the romantic and pre-romantic ages, but observing a bit how it is sung in the non-classical sorts of music and adding a bit of information about Europe's demography and its evolution since the Middle Age, some conclusions can be drawn.
Avoiding microphones by classical singing
I do only one distinction: only classical singers do not use gladly microphones, they find the use of such devices improper. The rest of the singers just does need it, but classical singers don't: they sing so to produce an extremely loud voice, a voice to reach the last row of the concert hall, in order to make their singing audible for the whole audience, even performing with a big symphonic orchestra.
Small audiences need no loud singing
Europe's population since the Middle Age seems to have been more or less –depending on wars and epidemics– the same amount of people until the XIX century, moment in which the population started to increase. I have to think that it was well entered the XIX century when classical singing was developed, in a time where concert halls grew bigger and sound amplifying systems had not yet been invented, because since the Gregorian singing –where monks sang for God and for themselves– until the XIX century, being the audience more or less the same, I don't see any reason to develop a very loud way of singing.
Classical vs non-classical singers
Classical singing should match very well the post-romantic repertoire, for that music was probably composed bearing in mind that way of singing. But when the matter is to perform earlier music some problems appear: problems of balance, problems of text and problems of pulse and tempo. Regarding the balance, classical singers are too loud, making instruments hard to be listened to. In order to produce such a loud voice classical singers use their throat and mouth in such a way that makes pretty difficult to produce the text, becoming it difficult to be understood: they produce a very loud vocalic sound with– depending on the singer more or less vibrato, to what they add the consonants, and it is because they are busy speaking the text that they are very often late. Often classical singers say consonants before the bit, bringing confusion to the timing instead of using consonants to clarify it. Other times, just not having enough time to speak consonants properly, the piece turns into a murmur, but most of the time simply a slower and free timing is created in order to give them the time to speak. Another problem that classical singers must face is the big amount of air that this way of singing requires: they must breath more often than originally was needed, bringing distorsion to the music. Considering their voice as "their instrument" classical singers use music to let them be heard, when it should just be the other way around: music should use singers to be. The normal practice is so that the orchestra must fit into the singer, instead of being the singer who fits into the orchestra.
Non-classical singers produce a very wide range of colours in their voices, and the text they produce is mostly clearly understandable. Further they do not have any problem to sing a tempo, just singing on the pulse of the music.
You can see a fantastic video where the two sorts of singing are directly to compare: Freddie Mercury & Monserrat Caballé sing "Barcelona".
Bach and the clavichord
I have heard very often classical singers complain about how difficult to sing J.S. Bach is, due to the big amount of text of his compositions. But Johann Sebastian's son Carl Phillip Emmanuel wrote that many singers preferred to sing accompanied by a clavichord. Even the Bachs had one at home, which they used to accompany their singing evenings. But clavichord is an instrument extremely not loud and it will not be heard when accompanying a classical singer, for these singers produce a far too loud voice that will completely cover its sound. That means that power was not at all a priority in the singing of that time, and so could they sing in a way where producing a lot of text was not at all an issue.
Listening to Jacques Brel's song "Une danse à mille temps" I find hilarious to listen to a classical singer complain about the big amount of text of Bach's compositions. Classical singers can though be completely right in that complaint; but instead of considering another way of singing they draw the conclusion that Bach is an example of a composer who wrote for the human voice with little knowledge about it... which I find a bit more than hilarious.
The basic idea: singers are to produce a text
When singing in a way where the priority is not power but the text that justifies the presence of the singer, becomes the text easily understandable, and speaking it requires then little effort. Being therefore this way of singing much more agile, it allows the singer to perform in more vivacious tempos, such tempos as another son of J.S. Bach said somewhere that his father preferred. And since this way of singing requires as well less amount of air, singers become able to sing longer frases, not causing then us to ask ourselves "why does this singer breath in such a place?"... For all these reasons, for the romantic and pre-romantic repertoire I would rather look into the non-classical way of singing. Without microphone in small concert halls.
Thankfully it begins to happen: Marco Beasley singing Frescobaldi.