Wow, A lot of good replies already posted here.
Taking only the original question of comparing a similarly priced MTH engine to a LionChief Plus engine, it will mostly come down to which you prefer... Mostly.
I think it only fair to point out the pros of going with the MTH engine before talking about LC+. The MTH engine has the ability to give you better sound and control if you run it with a full DCS system. If you are planning on installing DCS, and/or are looking for complete layout control, the MTH engine may be a better choice for you.
Without the full DCS system, as mentioned above, you get a conventional engine. You can pretty much match the functionality of the LC+ system if you add 'Remote Commander' for about $50. Also as was mentioned, that remote limits you to line of sight with the receiver. The remote commander can also only operate a single engine set to address #1.
With LC+ you can run as many locomotives as you like, however you may not like having so many separate controllers. Lionel is starting to address that issue with the multi engine remote now being offered.
I can not say how good the speed control is on MTH products as my experience is limited. I've done quite a bit of reading that engines are more or less accurate in their speeds within 1 or 2 SMPH of whatever speed they report, though that can be quite a big difference in some cases. I can say, with absolute certainty, that the speed control on LC+ engines is fantastic. The engine will move at the assigned speed regardless of variation in track power from 8 to 18 volts, though the very last, highest speed will not be available at voltages under about 14VAC. It is important to understand that LC has only 16 speed steps so there is not a lot of adjustment, but the low speed control is very good. These engines seem to start at about 2 SMPH. Each step is an exact percentage faster than the last. What percentage varies by model, but will be constant for that model of engine. My hudson is 33% per step, and my NW2 is 25% faster per step. in both cases you end up with 7 steps below 10 SMPH. From there things speed up quickly.
With LC/+ the remote is good for a good 50 feet through walls and all, and much more in open air. You can follow your locomotive anywhere you like and never have to worry about playing pong with a wall to get a command through. Also of note, if you do manage to lose signal, the engine will roll to a stop and beep at you. this could be good or bad depending what else is on the track.
When comparing similar engines it will mostly come down to which one you like the looks of better, if you already have a DCS system. If you don't, you'll have to decide if that is the direction you are going, or if you'd like something simple and bullet proof.
JGL