I opted not to write out my usual detailed analysis for several reasons. First off, I am super tired, Second, I'm not sure who all takes the time to read them (now is a great time to comment if you do, or if you prefer the write-ups OVER the videos). And lastly and most importantly, Wallop's upgrades are just really, really straight forward.
I will offer my personal opinion though....Tantrum Thrower is in my opinion the better path. The damage numbers are better and the fact that they occur in such rapid succession makes it a no brainer. Toss in (ha, literally toss in) the Soul Gem and how it upgrades the Hammer Toss that is addressed by Hammer Handler and all the stars align to take Tantrum Thrower. It is simple, plays easy, and will be an asset to both veterans and rookie players.
The only real reason to take Hammer Handler is if you either A-love the Hammer Toss (or equally hate the base hammer attack), or B-prefer long range combat. Obviously, this path is geared to keeping a long range, at least if you play the path to it's full potential. However, what I have seen in Trap Team rarely lends you to a true "distance" battle. You almost always have multiple enemies at varying distances. The other weakness with this path is that Wallop is simply not quick enough to retreat from said enemies to re-establish the path's benefits. It seems to always evolve into a scenario where Tantrum Thrower would be your best option.