Both are dialects of the same language, that is Classical Arabic/ Modern Standard Arabic. There are almost no differences in Grammar. However, there are important differences in vocabulary and pronunciation. The main difference is in vocabulary, since Tunisian Arabic has throughout history integrated words from sources specific to Tunisian history: the native Berber language, French, Italian, Spanish. add to that the parallel borrowings and influences of Egyptian Arabic and Gulf Arabic!
Important differences/ characteristics peculiar to each vernacular are found in pronunciation :Tunisian Arabic seems to have much shorter vowels. It allows consonant clusters in rendering words. Egyptian has much longer vowel sounds in words. Tunisian Arabic vowel rendering is much shorter. eg: Egyptian: kitaaab = TA: ktab (book)
kataabt = TA: ktibt (I wrote)
Here is a nice resource for Tunisian Arabic/ an ebook published on Kindle Amazon
"Tunisian Arabic in 20 Lessons", and 2nd edition "Tunisian Arabic in 24 Lessons" (with paperback version at createspace.com. it is very instructive, easy to follow and fun to read!
I searched it, found it in top 10 list in Amazon sales (categories Foreign Languages/ Arabic, Travel, Tunisia guides/Africa)
here is the link