Both are great games (I am happy and lucky to own both) but it really depends on what you are looking for.
If you want a short, brutal game that will likely make you a better player... play IM.
Even terrible and average players get something out of LoTR... usually a pity multiball or some such reward for games gone horribly wrong ( IM takes pity on no one). My 4 year old daughter likes LoTR the best right now out of my pinballs as she can start multiball .
Both have hard to achieve end goals, and I dare say that Do or Die multiball on IM is harder to achieve than Valinor as you have to make so many risky shots outside of multiball. That does not make it better, but I can't think of any other modes where NOBODY has ever claimed to make it to on stock settings. At least, nobody I know of.
I would say that IM is like a great pre-DMD game in terms of rules complexity, but somehow amped up on steroids. When describing IM to someone, saying it is like having an adrenaline syringe pumped into your brain is not far off from the truth. IM gets my heart racing in a manner that other games VERY rarely match, and it does so on a pretty consistent regular basis even after almost two years of ownership and regular play.
LoTR is the pinncacle of DMD heavy rules based pins. There is a lot to do; I do not play for Valinor but just see where the journey takes me every time. Unless you are a terrible player after owning this for a while an average "good" game will usually net you at least Fellowship Multiball, 1-2 two towers multiballs, and often RoTK multiball for a chance to Destroy the Ring (I am probably running about 40% on destroying the ring once activating this mode, I swear the flippers become weak on the very final shot ).
This is aside from starting at least several modes, possibly getting some bonus modes (gollum multibal, gifts from the elves etc...). There is a lot to see, and various ways to mix it up. However, there are no "good" short games on LoTR. A 4 minute game on LoTR gets you? A 4 minute game on IM can possibly get you into contention for a do or die shot... and the pressure is on .
That is enough typing for now... both are excellent games, in a sea of geat games to discover!