I have looked at the Kindle Fire (online) and saw a Yahoo comparison of that to an Ipad (not "pod") and the article seemed to be claiming that they were going to steal a huge chunk of market share from the iPad. But when I read the article, it didn't sound like it would to me.
Here is what (for me) would probably be the determining factor if I were in your shoes: cost. The devices themselves cost virtually the same amount of money. BUT, the Kindle comes (so I understand anyway) with an introductory free Amazon Prime membership (for like 60 days or something?). That is how you will purchase apps and books for the kindle. The ipods can access your already existing itunes account (if you don't have one, they are free) and load everything from there. BUT, there is a HUGE number of FREE apps that your kids can download and play. You can even load a Kindle app right onto the iPod and read books from the iPod if you want. But you see, the books are not free. Sure, there are books that are, but not likely many things your kids will want to read. We're talking the old classics that are so old that they are considered public domain. Little Women. Treasure Island. Moby Dick. All great books! But probably not what your 8 year olds will have any interest in. If you want to grab "Diary of a Wimpy Kid" you'll have to pay.
Now, the kindle is going to be bigger than an ipod also, which means portability (if you are sporting 2 of these things in the car) is going to become more of a nuisance. Every time you stop to run into a fast food place for the potty, you're going to have to either take the device with you or put it out of sight in the car. Bigger isn't better in those situations. Especially times 2.
I think as long as you get one of those neoprene cases for the ipod, (they keep them from slipping and sliding around on slick surfaces, or even just if your hand gets sweaty) then they will serve you very well. They come with earbuds in the package, too. :)
ETA: Both my kids have gotten touch's in the past year (my then 9 year old at Xmas last year, my now 13 yr old "earned" one at the end of the school year in May to replace the nano he had gotten the year before). They both LOVE them. And there are TONS of games and free stuff they can do. My 10 yr old even checks the weather before she gets dressed in the morning! They also use them plugged into a docking station (to charge overnight) to fall asleep to their favorite tunes. They take pictures. They make videos. They text (free apps for that, too). There is a LOT of capability packed into those little ipods. And I love Apple products anyway. My kids are not harsh with their electronics (DSlites, ipods, laptops, digital cameras, flip, etc)... and we have never had a problem with one getting damaged.