Well, there is confusion between these two hosting types & I am trying to strike out this confusion.
- Cost - In case of cost, wordpress hosting is costlier as compared to Linux hosting as the add-on plugins make the bill hefty. But in the case of Linux hosting, as per the price, you can at least get the benefit of cheaper hosting plans.
- Performance - When it comes to performance comparison, the Linux system does not slow down also, one year old, like other platforms, its performance remains the same. But in the case of Wordpress, if you dont upgrade timely, it may affect your hosting performance as you can't run your server on a same similar speed as it slightly affects your hosting speed performance.