First of all, MD5 is broken - you can generate a collision, so MD5 should not be used for any security applications. SHA1 is not known to be broken and is believed to be secure. Other than that - yes, MD5 is faster but has 128-bit output, while SHA1 has 160-bit output.
Update: SHA1 has been broken: a team of researchers at Google and CWI have published a collision - https://shattered.io/static/shattered.pdf
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