Most prefer CRF actions, Mausers, P14, Brno ZKK magnum or CZ magnum probably making up the bulk of the actions on these rifles, depending on calibre.
The main problem I have seen with a push feed action is actually not the feeding part but rather the extraction part. Many push feed actions have "tiny" extractor claws which can easily let you down in case of a sticky shell for whatever reason. Either shearing a part of the case of or just letting go of the case rim.
Another problem with regards to extraction on a push feed action that I have seen cause a reloading issue, is when a unfired cartridge needs to be extracted(due to a misfire). Most push feed actions rely on a spring loaded plunger or pin to eject the case from action when cycled. With an empty case most work fine many cannot "throw" an unfired cartridge out of the action. This can be made worse if the gun is tilted over to the left.
One advantage of a push feed action is that you can "throw" a loose round on top of the magazine or straight down the chamber and close the bolt, without fear of damage to the extractor claw. However with a CRF action you need to push the round into the magazine and cycle the bolt so that it feeds from the magazine to avoid damage to the extractor claw.
Remington M700 is a bad idea for a DG push feed action. The best push feed action I have used is a Weatherby Mark IV. Extremely strong with 9 locking lugs. I have a Custom built 338 Lapua Magnum on this action(It use to be a 460 Weatherby out of the Custom shop). I have cycle this action as fast as I can at different angles and has never not extracted or cycled a full round or a case. If I had no choice I would use this action on a DG rifle.
My own DG rifles(500 Jeff and 2 X 375 H&H-one soon to be 404 Jeff) are all on Brno ZKK 602 Magnum actions(controlled feed) and I have never had any issues whatsoever with them.
@ Ray B
If using the right bullet of the right calibre in the right rifle and you can hit what you are aiming at one shot is most of the time all is needed. More so on a charging animal than one departing, especially buffalo and elephant. On a departing wounded animal you basically have lower spine or hip joints as aiming points, which if done correctly will anchor the animal but not kill it outright so you will have to finish him off.
On a charging animal, provided you can see him of course, you can drop him with a well placed shot. Depending on species, either with a well placed brain shot or frontal or side neck/spine shot.
Since I switched from a 375 H&H to the 500 Jeff as my DG back-up rifle I have fortunately only ever needed one well placed shot on buffalo, elephant, rhino and lion. Buffalo coming and going, rhino coming, elephant coming and going, lion coming.
In the end personal choice, but I am sure you will find most prefer CRF actions.
Whichever you choose the most important is to check it, practice with it and sort out any issues that may arise before you use it as a DG back up rifle.
Another important tip I was taught when I started hunting DG, is to cycle ALL rounds I take with me for the day through my rifle, before the hunt begins.