I honestly have been a bit up in the air about which to use at times. I hope more people contribute to this thread, because I would like to know what some of the other players think about it.
Here are my personal obervations:
Ftilt has considerably longer range, so depending on your spacing, ftilt can be a better choice to hit when you are further away.
Ftilt is 3 hits, so if timed correctly you can hit people that like to spotdodge with the 3rd hit.
You can also use only 1 or two strikes of Ftilt to see how the opponent reacts. If they shield it, you can follow up with a grab. if they spotdodge or you hit them, you can finish the ftilt or switch to another attack. Most importantly, you should try not to finish ftilt unless you hit them because the last hit is relatively laggy and can be punished if it doesnt land. The last hit of Ftilt is also the one with the most range.
Ftilt will beat alot of arial approaches if you time it right too, so sometimes if an opponent is approaching from the air it is a better option that dtilt which would leave you open.
Dtilt, like others said, is a good "poke". A way of pressuring from a (somewhat) safe distance, and trying to punish your opponent's reaction. If you space it right, you can put people in a really bad place with this move. Often people will just hold their shield as you poke them, allowing you to run up and grab them. The idea is to predict what they will do (shield, roll, jump, etc) and punish it.
Dtilt is alot more spammable due to its IASA frames... it has alot less ending lag than ftilt, making it more safe on shield... just make sure you space it right because it can be shield grabbed fairly easily by characters with long grab range (DDD for example).
Keep in mind Dtilt makes you move forward with every strike, so if you are spaced perfectly on the first use, the second will bring you closer, and so forth. Keep this in mind when spacing it, because it can cause you to get too close if you don't. It makes it a good approach though, because you can space it a bit too far and toss a couple out to get you in the right range.
Thats all I can think of right now, hope that helps.