It really depends on the situation. Sometimes maintaining stage control gets you the kill. However, under normal circumstances it should be avoided unless you know you have the gimp against the specified character.
There are few instances in the game where you could forward throw for a tactical advantage, for example into a claymore mine thingy or to just initiate a tech chase onto a platform that would otherwise be unreachable by a down throw, but it's very information technical. You need to pay attention to damage and initiate the throw accordingly, however it won't always work if it isn't perfect. Forward throw has its limitations, but perhaps you could figure something out.
Up throw and down throw both have its advantages and moments. It honestly depends on who you're fighting and what can be done. At lower percentages it's best to keep down throwing and getting at it with simple follow ups, assuming you have the necessary knowledge and practice to initiate some good ones.
In some instances it's better to up throw simply because on some characters you can get a stream of combos, up airs, forward air, etc., and you'll initiate what's basically called sharking, a tactic most commonly used by Mk, but is great for most characters in general. It puts the opponent in a bad position above you, and you can keep juggling him or just finish it as you please. However, the same applies for the down throw. Most common combo is to d-air and juggle up and up which ends with the same results as an up throw, but more damage would be applied to your opponent. I have a strong belief that it really depends on the situation, but personally I use up throw for kills and down throw for racking damage.
This is a very controversial topic: Up air or down air? You decide. Yoshi strategies are just so diverse, you could live without a simple few tactics here and there. However so it is great to get to know more about the best of both worlds.
P.S. for most characters, the obvious use of up throw is to simply jump and up air. Guaranteed kill on most characters, not all as every character has their own weight.
Most Yoshi players are so diverse. See what works for you. I know that there are a few combos that I like to use, while others wouldn't, ex. RAR Bair to reverse-neutral B but many Yoshi players could live without it. As long as you've mastered the down throw, you'll be fine!
Hope this helps build this thread a bit. If anybody else would like to build upon this or make changes in convo please do so!