Interesting question you posed a couple pages back regarding the "dress diver." In this day and age, I think there is absolutely nothing wrong with some infatuation over a desk diver. Admittedly, they are kind of silly. But when you look at this hobby from the outside-in, it is silly. I mean, it is certainly more functional that an EOT function, sidereal time, or a moonphase.
And especially with the casualization of the workplace, these dress divers have just become more and more suitable for every day use. Even if I wanted to I could not wear a suit to the office. Or a tie for that matter. There are days where I am nothing short of mandated to wear jeans (lest I get looks of suspicion). For me, a watch like the JLC or that Blancpain makes much more sense. And let us not forget--although a dive bezel was created for... well, diving, it is an ENORMOUSLY useful function. Functionally I would take a dive bezel over a chronograph any day of the week. You can twist around the bezel ad nauseum and it won't do anything to the watch. But running your chronograph all the time is supposedly not the best if you do not want a steep maintenance bill, at least when the chronograph does not have a column wheel / vertical clutch. And even then...
In regards to those particular watches--I love the JLC, and the Bathyscaphe, I just don't know. I have not seen either of them in person, so you have to take what I say with a grain of salt. But I just don't LOVE the Bathyscaphe. I do think the extra sharp case is cool... I like the color of the dial... I could live with the day counter... but I do not know if I could live with the small-nippled dial. Everything just looks a bit small proportionately. But at the same time, it gives it a quirky feel. It does look better in pictures though:
As for the big three-big four thing. I just put VC, AP, and PP in the Big Three. They are known as such because of their storied pasts, the fact that they have been running for eons, and their propensity to work primarily (if only) in precious metals. AL&S deserves to be in the mix, but they are only 25 years old and they are German. Breguet, I would not associate with these brands. Despite having some nice models, Breguet (to me) is a creation of the SWATCH company. I love JLC, it is my favorite brand, but they make too many steel cased watches.