I have used metal filters similar to the linked model; however, a more correct statement would be
"taste all the flavors the coffee grinds have to offer"
This is both good and bad.
Metal filters are good in the sense that they allow you to experience a greater majority of the flavors that any coffee variety can offer (except for the Turkish grind coffee that will seep through the pores). This is particularly useful for Robusta coffee beans, where the flavor resides within the oils that would be trapped by the paper filters.
The downside is that metal filters allow you to taste even the un-pleasant(?) flavors too (I would probably be shamed for using that term). In a nutshell, I can say that paper filters are more forgiving than metal filters. If you make a modification or mistake in your coffee making process, it will be easier to taste the difference with metal filters compared to paper filters. i.e. if you use a metal burr vs. a ceramic burr you can taste the heat generated through the grinding process (if you're grinding >50g), or to a lesser extent if you pour 98-100°C water you may be able to taste it too.
My experience with paper filters have been positive, as I have primarily used off the shelf paper filters for my everyday cup of Joe, and Chemex filters for my fancy pants coffee (Chemex filters are thicker). While you will not be able to taste all the flavors when brewing with paper filters, you will still experience it through the aroma. A good example is to brew Italian coffee, which are generally more acidic, through a paper filter.