I believe, 大概，左右 both mean: roughly, approximately.
Why should/must 大概 precede and 左右 follow?
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Yes, both are meant approximation, but 大概 is a gross estimation - the house is approximately 900 sf; 左右 implies a calculated estimation - the house is 900 sf plus or minus.
大概 also can be used to express perceived uncertainty - 大概不好吧. 大概快到了. It is used in both measurable and non-measurable matters/objects.
左右 is used on the measurable matters/objects, like area, volume, dollar, distance...etc.
They can be used together, 這房子的面積大概在九十平方米左右 - The house's floor area is approximately 90 square meter, plus or minus. Note, in here, 大概 can be replaced by "大約", which is another term for approximation.
I can't give you why there is a difference in word sequence, but I can give you an example
The house is roughly 90 sq meters.
both correct, but
is not valid. This is actually a wrong/weird way of saying "there are 90 sq meters on (to) the left and also 90 sq meters on (to) the right of the house". Which should really be '这栋房子左边有90平方米，右边有90平方米' Still, what you are trying to say is not clear? is this the size of the house or the size of the yard to the left and to the right of the house
Now '左右' has the their original meanings when preceding, to (on) the left(左） and to (on) the right（右）.
But '大概' never means directions (left, right) It means
Informally, '大概' could also follow. E.g. '房子九十平方米（，）大概' （comma is optional, but this is just oral so doesn't matter..
but '左右' never precede in these kind of case.
There are many differences in grammar between English and Chinese, I would not suggest compare grammar. I would say Chinese grammar is not as systematic as English grammar, or it was a bad idea to create grammar for Chinese in English grammar style (just my opinion)
To my knowledge, there is no simple/systemic explanation of why there is a word sequence difference. Even ‘左右’ means roughly in this case, it is not an adv. in grammar definition.
Tl;dr: We can approach the question using classical Chinese.
左右 is originally a noun modified by the uncertain measurement that goes before it.
概 seems to only work as a preceding adverb.
For the sole purpose of justifying
左右 as being exclusively a complement (補語) but not otherwise (i.e., a preceding adverb / 狀語), I think there is no harm in looking at the word literally (which is also probably its etymology).
We know in classical Chinese
左右 as a noun means 'two sides', or more commonly, as a syndecdoche (借代) meaning 'courtiers':
The courtiers wished to slay Xiangru. But Xiangru berated them in return, his eyes wide open, and they all retreated. (Shiji 81)
With this in mind it is not hard to think of your phrase as
九十平方米之左右 (lit. the two sides of 90 sq m; meaning anywhere close to 90 sq m),
which actually makes
九十平方米 the preceding adjective (定語) of the phrase. Over time, however, it becomes more natural to treat
九十平方米–左右 not as a modifier–noun (定語–名詞) phrase, but a nominal word group–complement phrase (名詞詞組–補語).
This is in stark contrast to the stabler historical nature of
概 in classical Chinese) as a preceding adverb (狀語):
Now from what I have heard, Xu You and Wu Guang were supposed to have had the highest sense of right — why is it, then, that they are not even mentioned in passing in Confucius' writing? (Shiji 61, tr. Owen 1946)
不少 (not at the very least) and
概 (in brief) precede and are clearly adverbial on
見 (to be seen).
The positioning of
概 appears to be less flexible than say
盡 (you can have
盡訴 in modern Chinese; see my third point here). That is also observed in words like
概括 (but not
*括概), for example.
Reference: Owen, Stephen. An Anthology of Chinese Literature: Beginnings to 1911. New York: W. W. Norton, 1996.