I've read all of Fleming's outlines and listened to hundreds of hours of his lectures and I can't say that I've ever heard him recommend a particular writing style except for IRAC (or IAC if you're in a hurry), so I have no opinion about his recommended essay style. And I can't say that I remember if he even recommends a particular style. However, having said that, the basic IRAC format is recommended by everyone in one form or another so his is likely as good as anyone else's.
But if I was to pick a style from the vast number of bar prep programs I would have to pick BarBri's. That's because it's the one that most people take. And if the graders are going to catch some flavor from your writing and make assumptions from it, that's the one you probably want them to taste.
But, as I said to someone else recently, this is from someone who was unsuccessful in his first attempt at the Bar so take it for what it's worth. (;-)>
My own personal weakness, and what I'm working on right now, is condensing my analysis. I seem to be good at the IR&C part, but when I get to the Analysis, I either write way too much, or way too little. And I don't think that adhering to one style or the other is going to solve that problem. It's just something that I'm going to have to work out for myself.
So my advice is really no advice except to pick the one that works for you. If everything was equal then I'd say it doesn't matter as long as you know the material. But if I was forced to choose between your two options, I'd choose BarBri.
As for the MBEs, if you have a set of PMBR or BarBri books, use those for the MBEs. If those aren't in your personal library then I would suggest finding used copies on e-bay or picking up a copy of "Strategies and Tactics for the MBE" by Walton and Emanuel. The S&T book is only about $50 new so that shouldn't be too much of a burden. In fact because Walton and Emanuel's analysis is equally as effective as PMBR's (imho), you can probably pick up a copy of that book, and supplement with a used set of BarBri MBE books, for about as much as someone wants for a set of used PMBR books. I recommend that only because I thought PMBR's fact patterns were too busy (again, imho).
However, asking which MBE resource to use is like asking which oil to use in a new motorcycle. You're going to get many and varied strongly held opinions. Most people will tell you to use the one that fits your learning style the best. The only problem is that you don't know which one that is until you try each.
Most of the challenge associated with recommending an MBE tool is that they all work from the same core set of past released questions. Since the PMBR CF*, the Bar has changed the questions around quite a bit (again, imho). The ones that I remember from the July Bar Exam had a materially different feel (again, imho) than the ones you'll find that are derived from the NCBE released questions; which is everyone, including BarBri and PMBR.
The best way to beat the current MBEs may be simply to know all of the rules and their exceptions cold. I scored exactly on the California average for MBEs in the July exam (128 raw, 145 scaled) and I had been hitting averages in excess of 80% using the above mentioned pre-CF resources.
Again, this advice is from someone who failed the July bar so take it for what it's worth, and your mileage may vary.
(* Cluster Fu--dge) (;-)>