I own both a Mausingfield (M5) and a Fuzion (not the the Ti version) - both short action.
Both great actions IMO, I don't believe there is a bad choice between the two. The Mausingfield is CRF, which is a favorite amongst big game African continent hunters as it's supposedly more reliable and less prone to short stroking/double feeding from improper bolt manipulation (not something you want happening when you are being charged by a water buffalo). Not sure where you are hunting, this may or may not factor into your decision. Cocking is 105/-5, meaning that the bolt lift compresses the firing spring ~105%, and the firing spring gets released ~5% on bolt close. The idea behind this, is that if you are shooting on say a barricade, you can theoretically get more efficient follow up shots, as the gun will already be disturbed by recoil and sight picture slightly off, allowing you to eject the brass, get the rifle on target and be minimally disturbed by the bolt close. The bolt lift isn't much at all if its paired with a properly timed trigger, it doesn't feel any harder than the 50/50 action such as the Defiance or Lone Peak I have, and the light bolt close is really nice. One down side I've noticed with the Mausingfield is that the bolt lift gets stiffer than most other actions in the event of hot loads, dirty chambers, etc. Rail isn't integral, but its keyed and it's not coming loose, even if the screws somehow happen to back out. This allows you to change out rails if you decide later on down the road if you decide you need different elevation, but in practice I can't imagine anyone actually doing this. Interchangeable bolt heads if you desire to change bolt faces to utilize different cartridges. Toroidal lugs, which squares up the bolt face better to the chamber, with the potential to provide greater down range accuracy in theory - in reality, I doubt anyone can really shoot the difference.
The Lone Peak is push feed, nothing wrong with that unless you want it to be as fool proof as possible due to the above. Cocking is 50/50. Some people may prefer 50/50 over 105/-5 - it's really all personal preference. The geometry cocking cam on the Fuzion (and I can only speak for the "regular" and not Ti version, though I'm sure they are similar if not the exact same), is such that the initial ~10* or so feels slightly stiff, but "snaps" open after that. If you use a little momentum at the start of opening the bolt, it feels like it flies open. The Mausingfield is consistently smooth and light - not sure which one I prefer at this point, they both feel great in their own way. Fuzion has an integral rail - while I don't believe the Mausingfields rail is ever coming loose, it's impossible for an integral rail to do so.
I'm assuming the Ti version of the Fuzion is lighter than the standard Mausingfield, however there was a special run of "hunter" Mausingfield actions done for LRI, not sure if they have anymore or not. May be worth looking into, would be more competitive on the weight aspect.
At the end of the day, there's some distinct design differences that makes for some relatively subtle differences in the real world/field. I really don't know what action I prefer between the Mausingfield and the Lone Peak. They are both great, and I always speak highly of both of them. So many great options these days, that it's really hard to go wrong when spending this level of money on an action. Another action that would be worthwhile looking into is the upcoming hunter/titanium Impact, though I have no idea when it's supposed to be released, but supposedly "soon".