It depends on what you want to use your .300 Magnum for. If for precision shooting, go for a rimless case any day. The problem with a belted case is that the case is supported in / headspaced on the fit of the belt in its chamber recess. With full-pressure loads, the relatively shallow belt does change dimension and that changes its relationship with the chamber and hence the rifle. Apart from the tight fit / extraction issues after a number of firings mentioned by Dkhunt, none of this is of great importance to sporting shooters, and many belted magnums are inherently good performers in a well built rifle.
But, for the long-range precision shooter, this changiong dimension / relationship issue caused by the belt injects a possible inconsistency into the ammunition and its chambering fit - anything such is undesirable. When the .300 Win Mag and .30/338 Win Mag wildcat were widely used long-range match cartridges, shooters had their rifles built and sized their brass such that the case-shoulder was just off the front of the chamber and the front edge of the belt had a tiny gap between it and the chamber belt recess. In effect, the cartridges were converted to rimless headspacing. This generally, not always, gave better results than setting it up for normal belted case operation.
Remember what Holland & Holland's original objective was back in around 1912 when it introduced the first belted designs and rifles. British big game rifle builders liked rimmed cases (flanged as they called them in that place at that time) as they gave a very positive headspace even when the front end of the case had a lot of clearance around it in the chamber. Lots of clearance is decidedly desirable in big / dangerous game rifles as it gives reliable chambering and extraction even when the African sun has heated everything up to the point where metal is too hot to touch with bare skin. The conditions a lot of hunters, especially professionals, lived and worked in during late 19th / early 20th century was also often primitive so rifles and ammunition could suffer dust, dirt problems and ammunition see surface corrosion. Rimmed cases were great with break-open doubles, but presented all sorts of problems when bolt-action magazine rifles made by German and Austrian gunmakers challenged the English gunmakers. They of course used rimless cartridges. H&H married the two forms by creating the belted design of bottlenecked case cartridges. In effect, it headspaces like a rimmed design, but feeds as easily and reliably as a rimless design without having to have the fairly close relationship with the chamber that the rimless variety needs. This is such a successful concept, it's why the belted design has survived a full 100 years and nearly all dangerous game cartridges designed for turnbolt rifles still use it.
Cartridges for non dangerous north American and European game and for target shooting are a different matter entirely, and the widespread use of belted designs during most of the 20th Century in 'magnums' was never technically warranted and was a triumph of marketing-speak over good rifle and cartridge design. Yes, the 7mm Rem Mag and series of Wichester magnums that kicked off with the .338 in 1956 (I think) worked fine, but they'd have worked equally well with a similar case shape and capacity rimless case without the belted case's extra cost and potential problems. This was very much a US issue - continental European gunmakers produced some very large and high pressure / performance hunting cartridge rimless case designs and belted cases saw little use in Scandinavia and France / Germany etc. (They did in the UK though as after the huge post WW2 contraction in the English gun manufacturing industry, we Brits tended to look to the US for rifles and cartridges, not to our European neighbours.)
As dkhunt 14 points out, you have the .300WSM which although a smaller capacity design is a superb performer and it and the yet smaller Remington SAUM form the vast majority of .300 cal long-range precision custom rifles in use today.