The best primer is dependent on what powder you are using and the granulation of said powder.  My rifles generally like LP primers with Swiss BP.  Note! No all LP's are not created equal.

Keep on hav'n fun!
MikeT

I tried the Fiocchi LP primers this morning and they seemed no better or worse than my usual Fed 155 LMP primers. When I mentioned to a friend shooting near me that I was trying LP primers Vs LMP he said that the only difference between LP and LMP was that the cups were slightly thicker and there was no difference in the compound inside them, is this correct ?.
Owing to the current powder shortage here I'm forced to use Wano 3P powder which my rifle does not like much compared to my usual load of Wanp 2P, until I get my hands on more 2P I wont know for sure either way.
Mike.

I have an old Guns and Ammo article on this from the 1980s. Lots of different types were tested and the results were inconclusive. Generally, the magnum primers had thicker cups, but not always. Some brands  of standard primers gave more brissance than other brands magnums.
I haven't sen the article for many years, but I'll try to find it.
Fred

Cup thicknesses. Some magnums are, some aren't.

Not knowing if you were actually able to open the link I posted but is pretty clear primers are not the same and at times the none magnum primers can be hotter than the magnum primers themselves. 
Also and unfortunately German Salazar who provided these photos had a more extensive list of these types of photos. That pretty much covered all of the current primers both large and small and all the varieties available as well.
Again unfortunately he took all of his photos and his results off his Web. Site because he had decided to write a Book. He was also a very avid and a top competitor who unfortunately decided to no longer give his knowledge and extensive testing results away freely anymore.