It would take a long, thick book to describe all the differences between these two quite distinct dialects.
There are significant differences of vocabulary (especially words for everyday objects and actions), pronunciation and grammar.
As the authors discovered firsthand, arriving in Syria armed with a good knowledge of Egyptian leads to a lot of confusion and bewilderment!
Consider the simple sentence "what are you doing?"
In Egyptian, this would be "bitiﻉmel eh?", while in Syrian it is "shu ﻉam-t'saawi?" Note that almost everything is different: the verb "to do" (yiﻉmel vs. yisaawi), the word for "what" (eh vs. shu), the construction for "are ...-ing" (bi- vs. ﻉam-), and the position in the sentence of the question word "what" (at the end vs. at the beginning). In fact, the only common element is the "t" in the verb, indicating the second-person conjugation ("you").
Another good illustration is this direction to a taxi driver: "go straight ahead, and turn left at the square".
In Egyptian: "imshi ﻉala tuul w khush shimal ﻉand el-midan"
In Syrian: "ruuh doghri w liff yasaar ﻉand as-saaha"
Here the syntax is identical, but almost all the words are different. A native Arabic speaker, whether Egyptian or Syrian, would understand both, but it's very confusing for the foreign student.
Following are some of the major grammatical differences between Egyptian and Syrian:
Word order: in Egyptian, words such as "what" and "that" tend to be placed at the end of the phrase, while in Syrian they generally go at the beginning.
What do you want? ﻉayiz eh? (Eg) shu biddak? (Sy)
This book el-kitaab (Eg) da hal-kitaab (Sy)
Verb negation: in Egyptian, verbs are negated with the prefix ma- and the suffix -sh, while in Syrian only the prefix maa- is used. For imperative verbs, in Syrian the prefix is la-
I wasn't home makuntsh fi-l-beet maa kint bi-l beet
Don't forget matinsaash la tinsaa
No problem! mafiish mushkila maa fii mishkile
Continuous tense: in Egyptian, the prefix bi- is used to indicate continuing action (is ...-ing), while in Syrian the prefix ﻉam- is generally used (sometimes in combination with bi-).
I'm writing a letter baktib risaala ﻉam-akitb risaale
Future tense: in Egyptian, the prefix ha- is used to indicate a future action, while in Syrian the prefix bi- is used (and easily confused with the Egyptian continuous tense).
I will go haruuh bruuh
Active participle: this is used much more in Egyptian than in Syrian, which tends to use imperfect verbs instead.
I understand ana faahim ana bafham
Object pronouns: indirect objects (i.e. those preceded by a preposition) are used much more widely in Syrian than in Egyptian, which tends to use a direct object pronoun attached to the verb. If the verb to which the pronoun is attached is negative, the -sh suffix will be attached after the pronoun. This can create quite a mouthful, and gives Egyptian a distinctive sound.
As for pronunciation, apart from the -sh suffix sprinkled throughout Egyptian speech the most obvious differences are the hard "g" in Egyptian instead of the soft "j" in Syrian, and the Syrian pronunciation of the end of feminine nouns as "e" instead of "a" when preceded by certain letters.
There is also a tendency in Syrian to drop vowels and cluster consonants together, whereas Egyptian tends to follow the more classical consonant-vowel alternation.
Egyptians and Syrians will argue long and passionately about which dialect is closer to fusha or MSA.
The truth is that some aspects of Egyptian are closer, and some aspects of Syrian are.
Syrian vocabulary is often close to the MSA equivalent, while the Egyptian word is quite different. But then there are more words of Turkish origin in Syrian. Egyptian pronunciation is generally closer to MSA, with the glaring exception of the negative verb endings. Verb negation in Syrian is similar to MSA, with the Egyptian negation system radically different, but then the Egyptian tense system is much closer to MSA than the Syrian one is.