I don't own a JLC with the 899, but do have one with a 891. I also own a BP Leman with big date, and 100 hour reserve.
I agree with the other poster regarding the finishing on the BP being better, but I would also include the movement in my case (comparing it to the 891 in the JLC). In general I find the finishing on JLC movements somewhat lacking - not on all models but on most. Comparing it to the BP I have the anglage is quite rough and "unfinished" on the JLC. I think at first glance the finish on the JLC is quite good, but the fine details are lacking.
I can't say what the accuracy of the BP is "out of the box" since I bought mine used, but concerns over the slow beat rate are not real in my opinion. I did have a mainspring barrel break in the BP, and up until the symptoms of that surfaced it was by far the most accurate watch I owned (mixed in with a couple of JLC's, a GO, and a Sinn). I had heard that the movement in BP would be expensive to service but the total was $375 at an independent shop, so I was quite pleased with that. Right now the watch runs fast, but consistent, so it's just a matter of regulation - I just haven't bothered with it.
If I had to choose between JLC's current Master Control range and the BP's, the BP's would win every time on aesthetics alone.
All above IMHO.
Cheers, Al