They are mutually intelligible to a large degree. I know that from Per Langgård, one of the very few proficient second-language speakers of Greenlandic. He said that when he was in Nunavut, he spoke West Greenlandic, people answered in Inuktitut, and it worked quite well.
So there is a lot in common in basic words and the structure of the two languages. But when it comes to more advanced vocabulary, differences are clear. Greenlandic has a huge number of loan words from Danish, while Inuktitut is obviously influenced by English.
Sometimes the Danish origin of loan words is clear, e.g. sygeplejerske [ˈsyːəˌplɑjˀʌsgə] means ‘nurse’ in Greenlandic, just like in Danish, and sometimes it's harder to find out, as the word is adapted to Greenlandic phonology, e.g. palasi [palasi] means ‘priest’ and comes from Danish præst [pʁasd]. On the other hand, part of modern vocabulary is purely Greenlandic, such as qarasaasiaq [qɑʁasa:siɑq] ‘computer’, and that's probably understandable to speakers of Inuktitut (the Inuktitut version is ᖃᕋᓴᐅᔭᖅ /qarasaujaq/).
When it comes to basic vocabulary, perhaps the clearest influence of Danish is with numbers. Counting from 1 to 20 goes like this: ataaseq, marluk, pingasut, sisamat, tallimat, arfinillit, arfineq-marluk, arfineq-pingasut, qulingiluat, qulit, aqqanillit, aqqaneq-marluk, tretten, fjorten, femten, seksten, sytten, atten, nitten, tyve. As you can see, the Danish numerals are used after 12.