While the original answer gives you a satisfactory response, I feel it doesn't cover it in the detail that is necessary to address this question. It also contains some misinformation; Empoleon is not a physical attacker in any sense. Its physical movepool lacks the coverage available on the special side and its actual Attack stat is subpar. By the way, this answer is going to involve some constructive criticism. Don't take it the wrong way.
Before I go over an answer to your actual question, I just want to mention that trying to counter an Electivire with an Empoleon is plain stupid. You don't need to change your move set to counter a Pokemon simply because it beat your Pokemon, especially not if your Pokemon has an inherent type disadvantage against it. Empoleon is weak to Electivire, and there's very little you can do about that, especially given that Empoleon is slower than it is. It's much better to simply arm your team with a counter to Electivire that you can switch to if your Empoleon end up in the same situation again.
There are definitely ways to make your Empoleon more resistant to Electivire and Electric-types in general -- Wacan Berry and Earthquake are examples -- but these are still not worth using when you can simply switch out to another Pokemon that can deal with the situation more effectively. Those items and moves come at the cost of an item or moveslot that could be put to much better use, allowing Empoleon to play against a much broader spectrum of Pokemon. Overall, it simply isn't worth using Empoleon the way you want to.
I also want to mention that the idea you seem to have that you can plan your moveset to win in a very specific situation like you have with the Electivire at half health is flawed. The battle may not go in your favour, or you may decide on a better approach in the battle. You don't have enough control over the battle to be able to plan in advance like that. A broader, bigger-picture plan to counter certain Pokemon definitely works for some Pokemon, but planning your Empoleon to win in a situation like that is irrational. Empoleon simply doesn't have the tools it needs to counters its weaknesses on its own, unlike some Pokemon that have access to higher Speed, better moves and perhaps more efficient stats.
But I'll hear you out, and discuss why Aqua Jet is the better option of the two.
Aqua Jet is the superior option of the two moves you've listed as options. Brine is a niche move that has very limited use compared to other options like Hydro Pump or Scald, which both provide more consistent power as they do not rely on the opposition having half health. Brine is really a contradiction in itself -- you don't need x2 power to KO a Pokemon at half health. Aqua Jet's priority is more useful than Brine, especially if you already have a special Water move on your Empoleon (which you really should). At least Aqua Jet will allow you to pick off weakened threats and make up for Empoleon's low Speed; Brine, on the other hand, has little utility and is outclassed by most of Empoleon's other Water move options.
Though Aqua Jet is the better option of those two moves, it's still not really a move you should be using on Empoleon. Neither of those moves are particularly useful on Empoleon in the bigger picture, especially given the reason you want to use them, which I've already discussed isn't really worth it. If you want some ideas on which moves and sets you should use on Empoleon, I recommend you have a look at Smogon's analysis of Empoleon for some ideas.
tldr: Aqua Jet is the better option, but it's best you don't try to use Empoleon to beat Electivire in the first place.
