Python 2, 117 bytes

Takes a list of lists of digits a; returns one of its lists.

lambda a:max(a,key=lambda l:len(max(re.findall('1*',`[abs(x-y)%8for x,y in zip(l,l[1:])]`[1::3]),key=len)))
import re

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Python 2, 118 bytes

Takes a list of lists of digits a; returns one of its lists.

lambda a:max(a,key=lambda l:len(max(re.findall('1+|9*',`[(x-y)%10for x,y in zip(l,l[1:])]`[1::3]),key=len)))
import re

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Python 2, 117 bytes

lambda a:max(a,key=lambda l:len(max(re.findall('1*',`[abs(x-y)%8for x,y in zip(l,l[1:])]`[1::3]),key=len)))
import re

Try it online!

Python 2, 117 bytes

Takes a list of lists of digits a; returns one of its lists.

lambda a:max(a,key=lambda l:len(max(re.findall('1*',`[abs(x-y)%8for x,y in zip(l,l[1:])]`[1::3]),key=len)))
import re

Try it online!