There are two major factors governing the linguistic difficulty of Gawain as opposed to Canterbury Tales: dialect and poetry form. Chaucer is planted firmly in the world of the London clerical bureaucracy, clerks writing first and foremost for a "reading circle" type audience of other clerks, whose literary influence through "reading for fun" and through essentially running local and national bureaucracy did a lot to standardize the Midland-Kent dialects swirling around London into standard English.

The anonymous Gawain poet (usually known as the Pearl poet, although there are a few scholars who have questioned whether the two poems were really written by the same author), on the other hand, wrote in a northwestern-ish dialect, a version of the West Midlands dialect. That places the vocabulary a step removed from what we know in Chaucer--a step removed from the type of Middle English that would flow into early modern.

The second major factor is the type of verse. Canterbury Tales is governed first of all by meter with different rhyming patterns falling at the end of the line. SGGK uses alliterative verse, a specific format heralding back to Old English/Anglo-Saxon heritage that was undergoing a revival in just the part of England where SGGK's dialect places its author. The alliteration demands of alliterative verse not only suggest that a wider vocabulary would be necessary to make the patterns work--we think that using as wide a vocabulary as possible was part of the literary game and fun for authors writing in the style. I wish I remembered the exactly number--I think SGGK uses something like twelve or thirteen different words for "man."

As far as contemporary perceptions of language--yes, medieval people recognized both the general borders of many modern vernacular languages and the differences in dialect. Sometimes this is explicit. In mid-14C Germany, Heinrich von Nördlingen wrote to his friend Margaretha Ebner to tell her that he was sending a gift: a book by earlier mystical author Mechthild of Magdeburg. But, Heinrich said, her German was difficult so he had had a group of friends translate it into "our" German. Mechthild had originally written in Middle Low German (northern); the Bavarian-born Ebner's primary language was Middle High German. (It's tough to say whether medieval Low and High German qualify as "separate languages"--you can certainly cherry-pick individual texts that seem like it, but they'd be the ends of the spectrum while many people spoken and wrote somewhere in the middle).

The activity of scribes suggests a similar view. Monks and nuns acquiring books for their convents "translate" freely from what we would call one dialect to another. They are clearly quite adept with the dialect of their exemplar, but for their own convent, it's easier to pop the text into the local dialect.

Honestly, the biggest difference is just practice. SGGK is tough because of the vocabulary (which is apparent already by comparing scholarly translations!), but take something in the middle difficulty range between CT and SGGK--like Piers Plowman B. You're probably going to struggle at the beginning, but by the end, you'll practically be able to speak in Langland's verse and vocabulary.

I just got on reddit. If you don't mind an answer from a linguist, I think orthography explains 99% of it.

SIÞEN þe sege and þe assaut watz sesed at Troye, Þe borȝ brittened and brent to brondeȝ and askez, Þe tulk þat þe trammes of tresoun þer wroȝt Watz tried for his tricherie, þe trewest on erþe

Getting rid of the archaic letters: sithen the sege and the assault watz sesed at Troye the borge and brent to brondege and askez the tulk that the trammes of treson ther wroght watz tried for his tricherie, the trewest on erthe.

Now how much do you understand? I agree with @sunangainstgold that there are lexical reasons for why it is difficult.

There are forms of words like sithen 'since' where sounds were elided in the dialects of Middle English that went on to evolve into Modern English, and there are words like Tulk which did not make it into Modern English at all. borȝ means something like 'city' and survives in lots of Germanic languages as a suffix, but rarely as a word on its own.

There are also some morphological oddities. Watz is a pretty odd past tense form of be.

However it is not that different from the Canterbury Tales. Most of the differences are orthographic, not grammatical, phonological, or lexical. This is the main reason.

The author of Canterbury tales was using a form of spelling closer to what we use today.

Yes these would have been considered the same language. The difference is sort of like Croatian vs Serbian. One is written more commonly in a Latin alphabet while the other is written more commonly in Cyrillic. They are both more or less dialects of the same language though.

Can we get a translation of both of those sections?

THe biggest thing is Sir Gawain uses characters that you're unfamiliar with, and Canterbury tails use their more modern equivilent.

For example, there is the thorn (Þ) character. It was a separate character in middle and old english, but eventually fell out of use, partly due to limited character sets for some printers. You'll see "y" substituted for it sometimes, and that sound later became represented by "th". Gawain also makes use of the yogh (ȝ) character, which is from old english, and it was kind of a short g sound (like in gear, good, or ghoul). The reason why they fell out of use, is german printers often didn't have these characters (since they weren't used in German), and Normans didn't really like non-latin characters. Chaucer's earlier work included the yogh, but later not so much, partly because printers changing things between print runs. You're not seeing the original here.