Two very different machines made by two different manufacturers with two different layouts.
Both sound packages are pretty bad - so that's a tie
Both command "about" the same money - so that's a tie.
LOTR is considered one of the hardest pins ever made - I've played almost two hour games and after 6 years of owning still haven't reached Valinor. White water is easily beaten. (Doesn't make it any less fun)
LOTR has the option for a shaker that is code based not switch activated - Chalk one up for LOTR
LOTR can be a REALLY long game while White Water is a quick game in comparison.
I think that you should consider your current collection, how many fan layouts, how many quick game types VS long time games.
Variety is what makes a pin collection more enjoyable long term