Those look great! If you want to nitpick, the jacket could be a tiny bit longer, the gorge a tiny bit lower, the lapels a tiny bit wider, the chest a little roomier, and perhaps the buttoning point a tiny bit lower as well, but overall that suit fits you very well! You could go for roped shoulders as well, but the natural ones don't look bad either.
It's more down to stylistic changes than improving the fit, and if you're happy with the slim 1960s/madmen look you wouldn't have to change a single thing. The jacket and trousers are both equally slim, and look congruent. Why do you prefer the white one over these navy/grey ones?
If you want to use Luxire in the future, I'd send them this navy suit. The small changes you might want to make to the navy one will be much easier for Luxire to interpret than the big changes you'd have to make to your white suit. You could even go to a local tailor first and ask them if there would be a way to make the trousers drape better while keeping them slim, but I wouldn't worry too much about it. You should've shown these suits to begin with, would've saved you lots of time!