I would like to know what company makes the most accurate M-113 APC in 1/72nd scale?

I'm not a rivet counter but off the top of my head Italieri and Trumpeter come to mind. The former company has released a number of versions of the M-113 including the ACAV, M-163, mortar carrier (M-106), M-113A1 and a couple of others from the ESCI line that I can't recall. Trumpeter I believe has a few, ACAV, A1, A2 and A3 versions, plus their kits have a more complete interior including a detailed engine comparment. Somebody had an M-901 ITV version but can't recall which company it was. I'm sure there are a few others and it might be best to check through the lists at HENK of Holland Index Pages.

Cheers,
--Jan

Here's a comparison review of Trumpeter and Italeri/Esci:
https://www.onthewaymodels.com/reviews/Trumpeter/M113A3_prev.htm

the Trumpeter kit is best .. also S Model does as M113 that is also more accurate than the Italieri/Esci kit which is 30 to 40 year old moulds or more

The Italeri/Esci/Ertl kits are classics, but have deficiencies. Most notably single road wheels and lack of guide horns on tracks. The M163 variant is VERY basic with essentially a lump for the gun. Looks okay from 3 feet away. M901 has similar over simplification.

Trumpeter kits are nice. They have engine details, but no way to view them. The antenna guards are solid molded pieces. Personally, I'd rather than them missing as they weren't always present and removing them requires care.

S-Model kits are nice. tracks are simplified, but in many regards better than Italeri. A quicker build.

In general go with either Trumpeter or S-Model. Should you buy the Italeri kits don't expect the variants to yield much for kit bashing and don't spend much on them.