I tested Chrome and Firefox, both mobile on ssllabs.com:
Chrome
Cipher Suites (in order of preference)
TLS_ECDHE_ECDSA_WITH_CHACHA20_POLY1305_SHA256 (0xcca9) Forward Secrecy 256
TLS_ECDHE_RSA_WITH_CHACHA20_POLY1305_SHA256 (0xcca8) Forward Secrecy 256
OLD_TLS_ECDHE_ECDSA_WITH_CHACHA20_POLY1305_SHA256 (0xcc14) Forward Secrecy 256
OLD_TLS_ECDHE_RSA_WITH_CHACHA20_POLY1305_SHA256 (0xcc13) Forward Secrecy 256
TLS_ECDHE_ECDSA_WITH_AES_128_GCM_SHA256 (0xc02b) Forward Secrecy 128
TLS_ECDHE_RSA_WITH_AES_128_GCM_SHA256 (0xc02f) Forward Secrecy 128
TLS_ECDHE_ECDSA_WITH_AES_256_CBC_SHA (0xc00a) Forward Secrecy 256
TLS_ECDHE_RSA_WITH_AES_256_CBC_SHA (0xc014) Forward Secrecy 256
TLS_ECDHE_ECDSA_WITH_AES_128_CBC_SHA (0xc009) Forward Secrecy 128
TLS_ECDHE_RSA_WITH_AES_128_CBC_SHA (0xc013) Forward Secrecy 128
TLS_RSA_WITH_AES_128_GCM_SHA256 (0x9c) 128
TLS_RSA_WITH_AES_256_CBC_SHA (0x35) 256
TLS_RSA_WITH_AES_128_CBC_SHA (0x2f)
Signature algorithms
SHA512/RSA, SHA512/ECDSA, SHA384/RSA, SHA384/ECDSA, SHA256/RSA, SHA256/ECDSA, SHA224/RSA, SHA224/ECDSA, SHA1/RSA, SHA1/ECDSA
Firefox
Cipher Suites (in order of preference)
TLS_ECDHE_ECDSA_WITH_AES_128_GCM_SHA256 (0xc02b) Forward Secrecy 128
TLS_ECDHE_RSA_WITH_AES_128_GCM_SHA256 (0xc02f) Forward Secrecy 128
TLS_ECDHE_ECDSA_WITH_AES_256_CBC_SHA (0xc00a) Forward Secrecy 256
TLS_ECDHE_ECDSA_WITH_AES_128_CBC_SHA (0xc009) Forward Secrecy 128
TLS_ECDHE_RSA_WITH_AES_128_CBC_SHA (0xc013) Forward Secrecy 128
TLS_ECDHE_RSA_WITH_AES_256_CBC_SHA (0xc014) Forward Secrecy 256
TLS_DHE_RSA_WITH_AES_128_CBC_SHA (0x33) Forward Secrecy 128
TLS_DHE_RSA_WITH_AES_256_CBC_SHA (0x39) Forward Secrecy 256
TLS_RSA_WITH_AES_128_CBC_SHA (0x2f) 128
TLS_RSA_WITH_AES_256_CBC_SHA (0x35) 256
TLS_RSA_WITH_3DES_EDE_CBC_SHA (0xa)
Signature algorithms
SHA256/RSA,SHA384/RSA, SHA512/RSA, SHA1/RSA, SHA256/ECDSA, SHA384/ECDSA, SHA512/ECDSA, SHA1/ECDSA, SHA256/DSA, SHA1/DSA
SHA384 is seemingly unpopular. Have not seen it in the wild. Firefox (NSS) and Chrome (WebCrypto) have some problems implementing those strong ciphers.
Firefox: https://bugzilla.mozilla.org/show_bug.cgi?id=923089
Chrome: https://groups.google.com/a/chromium.org/forum/#!topic/chromium-discuss/ufzO8NhttaA