One of the biggest problems I have with handheld consoles is hand cramps. It seems that they are not designed for larger hands and long-term playing. As a result, I have found a couple of comfort grips that have worked well for me.
I never required any kind of grip on the Nintendo DS or original 3DS. Those were much smaller units and felt just fine in my hands without a grip. However, with the 3DS XL, this changed. The device is significantly larger, which is great for screen real estate, but it just wasn’t comfortable to play. Fortunately, I discovered the Dreamgear comfort grip fairly quickly. It’s a soft rubber that slips over your 3DS. It’s actually two sleeves, one for the top and one for the bottom. It also helps to absorb some shock if you drop it. I also have one for my New Nintendo 3DS, which is necessary because the switches and buttons are moved around. You have to take it out of the sleeve to change carts, however, which you didn’t need to do with the 3DS XL.
The PSP is terribly uncomfortable to play without a grip. I recently got the Nyko PSP Charger Grip. It’s hard plastic, so it’s not as cushy as the Dreamgear, but options for grips for the PSP are surprisingly limited. I got this one because it’s got an extra battery pack in it, so you actually charge the grip, which charges your PSP. It’s comfortable enough and extends play time in more than one way.
I found both of these on amazon.com. If you’ve experienced discomfort while playing either the PSP or 3DS, those are what I recommend.