RSA for compatibility, ECDSA for security and speed. Tho even Windows Vista and forward, Internet Explorer 7 and higher, all versions of Chrome, Firefox 4, Android 3 and higher supports ECDSA. There's really no reason not to use ECDSA today.
DSA is an old standard, similar to RSA in security but approved for government applications with slighly higher security requirements than RSA. Some more information below:
Digital Signature Algorithm, or DSA, uses a different algorithm for signing and encryption to RSA, yet provides the same level of security. It was proposed in 1991 by the National Institute of Standards and Technology (NIST) and adopted by the Federal Information Processing Standard (FIPS) in 1993. Since then it has gone under four revisions.
A DSA certificate makes it easier to keep up with government standards as it's endorsed by federal agencies - including the impending move to 2048-bit key lengths. You can even run RSA and DSA simultaneously to enhance your security further. Apache servers, for example, can run RSA and DSA certificates simultaneously on just one web server. This will benefit businesses seeking to maximise their ecosystem reach for their business correspondence.