I have three questions:
- Would you use HMAC-SHA1 or HMAC-SHA256 for message authentication?
- How much HMAC-SHA256 is slower than HMAC-SHA1?
- Are the security improvements of SHA256 (over SHA1) enough to justify its usage?
That is a semi-serious answer; both are very good choices, assuming, of course, that a Message Authentication Code is the appropriate solution (that is, both sides share a secret key), and you don't need extreme speed.
Those sorts of crypto performance questions are quite platform specific, and so it's hard to answer definitively. In my experience, I've seen SHA-1 (and hence HMAC-SHA-1) be about 30% faster than SHA-256; Your Mileage May Vary, of course.
Of course, the obvious comeback is "how much is this performance delta important to you?". That rather depends on how fast you're adding/checking integrity tags.
To the best of our knowledge, there is essentially no security difference between HMAC-SHA256 and HMAC-SHA1; with a sufficiently long key, both are impervious to brute force, and with a reasonably long tag, both will catch any forged messages with the expected probability. There is a known weakness to SHA1 that allows someone to compute a collision in less time than expected; there is no known way to apply that to HMAC-SHA1, and so there are no known methods of attack (other than, as I mentioned just now, brute force, and guessing the tags randomly).
I would use HMAC-SHA256.
While poncho's answer that both are secure is reasonable, there are several reasons I would prefer to use SHA-256 as the hash:
The only potential downside is performance, but it's probably not significant in most HMAC use cases, since where performance is important you can find even faster MACs to use instead. So I would consider the above reasons sufficient in most cases to justify using SHA-256 as the HMAC hash.