I have SRAM Rival with double tap shifters on my road bike. I really like them. With double tap, you use the same shifter to go up and down your gears. I think with Shimano there are two shifters, one for up, and the other for down. I don't think one is better than the other, just a matter of what you are used to.

The bigger difference with Apex versus Tiagra is that Apex has larger rings on the cassette, I think it goes up to 32. Not sure if Tiagra goes that high. I have a 32 on my Rival setup and like having the ability to get lower gearing when climbing than what you would normally be able to do, as I think most compact crank setups only go up to 27 or 28. Not sure what Tiagra can do.