Why does Borden want to change the knot used in the trick?

The answer is given in the scene following the first time we see Julia performing the trick.

CUTTER I saw you drop the knot again, Borden.

JULIA I think I had my wrist turned.

CUTTER (ignoring Julia) Some nights you just can't get it, can you? If that knot slips when Julia's on the hoist she'll break a leg.

Cutter is criticizing Borden for being careless when tying the knot and risking an accident. (We see Borden having to tie the knot twice in the scene earlier).

Borden then suggests the Langford Double would be better, which Cutter rejects as he says it would be unsafe under water as it would swell and lock.

I think one of the twin brother is not good at tying the knot, which is evident as said by Cutter:

"Some nights you just can't get it, can you? If that knot slips when Julia's on the hoist she'll break a leg".

So that night the twin brother who is not good at tying simple knots tied the knot. Both of the twin brothers are probably good at tying Langford double, so Borden proposes a change in the knot which eventually Cutter rejects.

In the next show of the same trick, as per answer here the twin brother who is good at simple knots is present and he tied a simple knot (also gave a glance to Julia without knowing the discussion his twin brother had after the previous show regarding the knot). Julia thought (per glance from Borden) that its a Langford double and underwater in the tank she tried to use Langford untie technique, but by the time she realized that's its a simple knot it was too late.

I think Borden and Julia both were trying to do something new. You see from the very first starting of the movie, Borden speaks one thing again and again in the movie that the tricks they use is becoming overly boring and that they should need a change or a break to let the viewers enjoy a new category of tricks, not the conventional tricks. The way Borden makes suggestive eye contact with Julia on the day of the accident to which Borden nodded, I believe Julia let him took the risk for both of them. They were trying to do something risky. Maybe in this way they were trying to prove to Cutter that a lit bit risky step is not that bad and might result in a good fresh trick.

Bordon's character resembles a man who wants to get ahead. He doesn't want to keep being an assistant. He wants to be a great magician himself. For this he has to learn tircks. For learning tricks he has to do experiments. In a scene we see him throwing a cage with a dead bird inside it. This proves that he is constantly trying things and failing too. This was the case with the knot. He did an experiment, but failed.

The use of foreshadowing when Borden killed the bird is displayed when he crushed the cage for his magic trick. Compare this with how Angier and Cutter treat their bird: it comes away unscathed and alive. This also reveals his character's darkside, making it highly likely that he indeed sabotaged the knot to lead to Angier's wife's death. Everything Borden displayed, pre-drowning, supports this thesis: he was complaining how their magic show was dull and lackluster. This gives him all the motive to come to the conclusion that he saw it beneficial for her to die during the magic show. It was a ploy to attract attention at any cost as a gimmick for his more daring and risky brand of magic.