Some believe the large, non rotating Mauser type extractor is superior. It may be so, but millions of guns over many decades has not shown any significant practical inferiority to the push feed designs.
The only advantage I can think of for a Mauser-type claw extractor is the larger claw of the extractor is less likely to slip-off a fired, stuck casing.
If you feed your rounds from the magazine the claw extractor will last longer than a push feed. If you require the claw to snap over the cartridge rim it will likely break around the same time as the push feed extractor. I have had a M1903 extractor break in this way and others have had claw extractors break. The early Ruger pseudo Mauser M77 had a claw which snapped over the rim. The early M77 were in fact push feed actions with a Mauser looking claw extractor but it was not controlled round feed. You spend some time looking on the web, there are a number of posts from owners looking for one of the those rare extractors, because theirs broke!
When I pulled targets with AMU, USMC, and Army Reserve guys, their M16's wore out push feed extractors. These guys fired thousands if not tens of thousands of rounds per month. Other things wore out to, so it is not a knock against push feed extractors. The push feed M70 would wear out its extractor. Instead of holding the cartridge against the bolt face, the extracted cartridge would fall off into the action causing a stove pipe jam. I helped a guy with a M70 push feed replace his extractor on the firing line. The match director was a gunsmith, had a box of M70 extractors, and we carefully made sure the spring loaded pin did not roll out into the grass as we changed the extractor out. M70 push feed extractors are different, I don't know how to categorize them, but there are model variations. M700 Remington extractors are one of the weakest push feed extractor designs. They wear out and you have to make sure the bolt face does not have crud impacted into the recesses because the Rem 700 extractor will break if it can't flex.
I like the claw. Primarily I like claw extractor mechanisms because I can open the bolt, pull it back, and the actions do not have a spring loaded ejector which flings the brass way out in front of the firing line. Instead I can just bump the case out of the action on to the bench.
Dumoulin Mauser 98 extractor claw
I like M70's. It is always a hoot when the things shoot straight, all the way out to 600 yards. Now who was it that said the 30-06 can't shoot straight?
I have one of the PBR's, Patrol Bolt Rifles. These were the last M70's assembled at New Haven, I think the parts were made elsewhere.