So I too was confused about the difference between suus and eius, and came across this question and its great answers.
TL,DR; suus refers back to the subject of the main clause as the possessor, whereas
eius refers to someone else:
Canem suum videt
"He sees his (own) dog", versus:
Canem eius videt
"He sees his (= someone else's) dog".
So far, so good.
Thinking further about the two words, I realized that suus is basically an adjective and as such, agrees in case, number, and gender with the noun it's attached to; whereas eius acts as a noun, the genitive of is/ea/id, so it's by definitition always in the genitive (otherwise it couldn't express possession); only the adjascent noun takes the case the sentence calls for (see canem in the examples above).
The adjective suus/sua/suum can appear on its own and act as a noun (substantive), inflected in the appropriate case:
"He sees his own (dog, or any other unspecified masculine/neuter thing)"
But we cannot say:
to express "He seems somebody else's (dog, or any other unspecified masculine/neuter thing)"
because eius is not in the accusative and cannot express a direct object of videō/vidēre, (I might be wrong here, please correct).
Similarly, eius can't stand on its own where a nominative is called for. So we can say:
Canis eius est melior
"His dog is better"; we must use eius and not suus because the subject of est melior is the dog, not the owner, right? Maybe I'm wrong here becasue there's no main/subordinate clause involved...?
So the question is: How would we tranlsate "His is better", without specifying what the possessed thing is? I believe we cannot say
Eius est melior
because again, the subject calls for a nominative.
So perhaps it can be:
Ille eius est melior
("That unspecified thing of him is better")
although I'm not sure if this is idiomatic Latin.