You want to create four groups of two mirrored drives (RAID 1), then stripe the four groups (RAID 0). This is RAID 10, sometimes called RAID 1+0. Because dropping a drive out of a mirrored array is not fatal, you could, in theory, lose one drive in each mirrored pair and still be safe.
In your other setup, you would create a four-drive stripe (RAID 0), then mirror those two stripes (RAID 1). This is RAID 01, sometimes called RAID 0+1. You'd basically find yourself with a two-"drive" RAID 1. A failure of one drive would effectively make three others inoperable. The chances of two simultaneous failures being on opposing sides of the mirror are dramatically increased.
Performance characteristics of each are usually around the same, but 1+0 is considerably less risky. Remember, regardless of configuration, you're still writing and reading data from the same effective number of striped segments.
If you aren't horribly write-heavy, don't discount RAID 6 or even 60 as an option, both of which are available in the 9240. With eight drives, RAID 6 will give you more space while allowing two drive failures. RAID 60 will allow up to four drive failures, while giving you the same capacity as RAID 10, while also not caring about which specific drives have failed.
Also keep in mind that some RAID cards refuse to do writeback caching unless they have a BBU. The writeback cache can be a huge performance boost. I'm not sure if the 9240 is one of those cards. Newer generations of the 9260 have this restriction, for example.
Also, I urge you to review the 9240 manual. Section 2.6 has a great overview of the available RAID levels and their benefits/drawbacks.