Pros
The barrels on the BM are new-made for the 7.62x51 NATO round. The advantage in the BM-59 is that all parts are new and they are all Military, not just milspec, but made by the original manufacturer on the same equipment for the military. They are very much Garands, and did everything the M14 promised to do, and that was make an improved Garand and use existing Garand machinery.
The M1a is more common and extra parts are easier to get. Military magazines (the only decent ones) are easier and generally cheaper to get.
Cons
The BM-59 will be more difficult to get parts for, though they are available. Magazines are more expensive (but not a whole lot more expensive, perhaps $20-$30 more).
The M1a is largely becoming a rifle of after-market parts as the supply of original military parts dwindles to nothing. Many military parts will be used. They are commercial rifles built on military patterns, but are fundamentally more aftermarket than military. That is not by itself a problem, but the M1a or m14 clones are not made by the folks who made the rifles originally. Real military mags are becoming cheaper, but still aren't anywhere near as cheap as FAL mags, and while half the cost of bm-59 mags, they are still pricey.
The really important thing is what kind of accuracy difference might be expected? The standard m1a I owned several years ago was not nearly as accurate as my CMP Garand (which was a used rifle). It was an accurate rifle, to be sure, but when it couldn't hold a candle to a used military rifle on similar surplus ammo that was 1/3 the price, seemed silly. But, 5 years later, I'm thinking I would still like to have one, but came across the BM and startd thinking about it.
Ash