Alex, it's not so much a matter of 'accuracy' (being pedantic, we're actually talking 'precision'). Large and small primer Lapua 308 brass is in my experience with several recent lots, to all intents and purposes identical, primer pocket and flash-hole dimensions aside. That is, they have the same internal (water) capacity, same weights, same neck thickness. There are good production lots, not so good, and downright superb in both types.
So, all other things being equal, they'll shoot same size groups in a given rifle with a given powder / bullet combination with a bit of charge weight adjustment as Scott Harris says - ~ a half grain.
The reason the Palma case was developed and adopted and has been allowed to use the the closely guarded 'Palma' name is that the company was asked to produce modern copies of the old Remington UBBR brass by the US Palma teams. The raison d'etre not being to produce higher MVs with the usual 155gn Sierra MK + H. VarGet combo, but to reduce MV spreads and ES values. When you're shooting a ballistically marginal bullet for 900 / 1,000 / 1,100 yards competition at ~2,950 fps in some of the hardest fought international shooting matches around, you want as small a velocity spread as possible. Variations = Elevations in any very LR shooting, but especially when your bullets are transonic and maybe even subsonic at the longest distance. That was the objective and the trial Lapua cases produced the goods, the US Palma teams adopting it, and Lapua putting it onto general sale a year or so later, also permitted to use the 'Palma' name as a thank-you. In Palma loads, ES values are reduced by a third or more over standard LRP brass.
It also works in FTR where people are developing loads that often produce single-figure spreads - that's ES, not SDs I'm talking here. On top of that, some hefty loads are being used successfully to get some seriously high MVs with all bullet weights. And the cases last too. They ARE much stronger in the case-head area than their LRP siblings, but I have a suspicion that the small flash-hole and different primer flash characteristics also change the early charge burn behaviour in some beneficial way. Or, maybe not ... and people are just running near proof loads and getting away with it.
Even at some of these very warm loadings, brass life is very good. I know people well into the teens of firings with Palma brass at MVs that 308 simply shouldn't be able to produce and they've yet to scrap a case except those that they over-cooked in load development. FTR shooters have suddenly become very interested in annealing - they didn't need to 'Before Palma' as pockets opened up and the case was scrapped before work hardened shoulders and necks became a serious issue.
I'd say that Palma brass adds 50-100 fps MVs for 155s. So far as the heavier bullets and slower burning powders go, I don't know anybody shooting 185-215s at GB national level who still uses standard brass. I can't say what Palma brass is 'worth' here, because there is little LRP brass data around now to provide comparisons and people were well into using Palma cases before the 200-230gn Hybrids appeared.
Another pointer to their worth with 'heavies' is that there is also 100% adoption by GB and GB Commonwealth 'Match Rifle' competitors. This is a 1,000 yard plus discipline for the 308 but shot with a lighter barrel than FTR and other differences, the main one being the use of the standard Fullbore LR target centre with a 1-MOA 'V', 2-MOA 'Five' and so on. Where ranges allow, MR is shot at up to 1,500 yards such as in international matches in New South Wales, Australia a few years back. These guys throat their chambers RIGHT out and use some fearsome heavy VLD / Hybrid loads - velocity is king in this discipline.
Downsides? If ignition is difficult - a hard to ignite powder in cold conditions - the performance may fall right off. I have seen some loads that simply didn't perform in temperatures just over freezing, yet they'd be OK with a powder from the same company - eg Viht N140 performing poorly, but N150 being OK, in a side by side test session. in theory, they shouldn't work well with older ball powders, yet in side by side tests I got higher MVs and smaller ES values from a Hodgdon H414 load with the Palma brass over standard brass with F210Ms on a chilly winter day - the total opposite of what I'd expect.
The other pointer to their benefits is that in some parts of the world, there is a thriving out of season activity in reforming Palma 308 to other calibres - 260 Rem, 7mm-08, 6.5mm Hornady Creedmoor even - for top velocity and precision competition or LR sporting loads. The Kiwis and Aussies seem to have latched onto the benefits in cartridges like 260 Rem much more than us Brits - can't speak for US tactical and sniper / F-Class etc shooters. It may be that there is a lot less use of the larger case sevens in these countries, so there is greater need to optimise the smaller numbers' performance.