What is the significant difference between using a paper filter over a reusable metal mesh filter for Chemex?
A paper filter is a true "filter" in that it basically only allows liquid to pass through. This means that you will have no sediment in your coffee, if that is a concern to you. Paper filters are absorbent though, so some of the flavor compounds of the coffee will be absorbed into the paper, and some other compounds as well (a chemical in coffee that causes a rise in cholesterol is absorbed by the paper). The paper can also lead to a papery flavor in your coffee.
Metal filters only filter out particulates of a certain size, so you will frequently end up with a layer of "sludge" at the bottom of your pot. Metal filters should be non-reactive though, so they will not add a flavor to your coffee and will allow everything extracted from your coffee to pass through.
If cholesterol isn't a concern, I'd say try both and see which you like better.
AHHH! Now I get it! I've used both. A lot. The fact is, I don't taste a difference. I only pick one over the other for convenience or economics. It's cool to just dump a disposable filter, no muss, no fuss. But disposable filters cost money. The other one is already paid for. Funny thing, I've used nothing but the metal one for over a year. It would cost me $5 to replenish my supply of coffee filters, it seems I always have some other way I'd rather spend that $5. One tiny caveat is that the metal type will leave a tiny bit of sludge in the bottom of your carafe. Don't pour it into your cup and you'd hardly know it was there.
Paper filters, essentially allow water to pass through with the lack of sediment in your brew. They absorb well enough, but at the same time can absorb some of your coffees flavor. I've heard of many people complaining about a paper-like, or chemical-like taste to their coffee when using a paper filter. Everyone has their own opinion and tastes though when it comes to this.
Metal filters, or the stainless steel filter route can be handy for a number of reasons. The lack of waste after brewing is nice to have. The fact that they're reusable is quite handy and can save you a lot of money in the long run. One of the most important aspects of a metal filter is the retention of oils in your coffee. These filters can give you a nice full-flavored cup.
Hope this helps and happy brewing. Feel free to hit me up for any questions, recipes or roast suggestions.