Striping just spreads the data over two drives equally, so half goes on one drive and other half on the other drive (assuming you are only using 2 drives for the stripe). Problems with striping is that If one drive fails, you are kind of screwed unless you are using a stripe with parity drive system. With that method, the parity drive can be used to recover files.
The mirror system is nice because every file is duplicated on both drives, so if one fails, you have a complete recent backup on the second drive. Disadvantage of the mirroring system is that well you can only use half of your storage space. You have two 80GB drives, with the mirror system, you can only use 80gb of that, while if you use the stripe config, you have the full 160gb.
Its a toss up on which config you want to do, there are other configs too, each with their own advantages and disadvantages. With only two drives, your possibilities are a little narrowed, but the true power of raid comes in with servers with lots of hard drives
On a small personal note, my roommate had a stripe config setup and then one of his hard drives failed and we tried and tried and tried to recover ANYTHING from it, and we were unsucessful. I am staying away from raid for right now until i get a huge mass of hard drives

But that is just my personal beef.