Solid state or Mechanical relay
SSR- have to get rid of heat (around 10W for 10A), probably more expensive (including heatsink), fairly bulky, failures are difficult to predict, but usually in 'on' state. Failure likely in case load is shorted unless expensive fuse and overrating are both present. Snubbing circuits leak significant current when 'off'. Current carrying capacity decreases rapidly as ambient temperature increases. 

SSR+ long life if conservatively rated and protected. Good electrical isolation and low electrical noise comparatively (especially for resistive loads and zero crossing type switching). No acoustic noise. Usually (for AC types) just normally open "form A". 

Relay- will wear out with a fairly predictable life of 50,000 operations and up- with derating millions of operations are possible but eventually the relay wears out either from the contacts wearing out or from mechanical wear. Draws perhaps 1/3 to 2W from the driving circuit, and is an inductive load. Switching causes more electrical noise. Makes an audible click or clank every time it operates. 

Relay+ often very inexpensive and compact. Acoustic noise can be an advantage. Multiple contacts are possible with little or no added cost (eg. normally closed or a second set of changeover form C contacts). Failures are usually 'off' state (N.O. contact) if the relay is properly rated. When off isolation is usually very good (no leakage current). Possible to switch both sides of AC line (or all three phases) where that is required using a single device. Very high temperature versions available for a premium.