I've always preferred tempered glass screen protectors with 2.5D edges, chemically treated if possible. I had used PET film for my n3DS XL, but had been getting bad luck finding a good set for the regular n3DS I just got a couple weeks ago - Xtreme Guard sent me the wrong protectors, another company sent me poor quality skins, and there is nothing I could find for the top screen around town.
I decided to give AFUNTA a try. Here is their link on Amazon, but I found a set on eBay for around $15:
https://www.amazon.com/gp/product/B01N0K7IBT/ref=ox_sc_act_title_2?ie=UTF8&psc=1&smid=ATQWPUY890LK5
I have tempered glass on my PS Vita, as well, and was very impressed with the result. I've been cautious with the 3DS because I've read the protector is a little thick, and touches the case before the rubber bumpers do. This is true for the n3DS, in my experience, but very very slightly. You could hardly tell unless you close your 3DS very carefully, which I usually do.
Screen quality looks great. I don't even really notice glare when the screen/s are on for both systems, or not enough to matter. The display seems natural, and oil or dust both wipe off very easily. No scratches on the PS Vita protector so far, and I've had it for about a year already.
I highly recommend glass, but it is little thick if that bothers you to have it press against the screen frame a little when closed.