My first question would be if you are looking at a Gen 3 MPX or an older Gen 2. If a Gen 3 I will tell you that one of my main shooting buddies (GM) Just switched from years of shooting JPs exclusively to the new Sig and he is amazed by it. Not just the recoil/dot movement but the balance of the weapon as well.
My personal experience with a Gen 2 MPX and a JP is that above any other weapon, in any division the MPX leaves me giggling like a child at the end of every stage. If it runs. I went down the dark path of trying to find the softest, flattest, 125.1PF ammo. The people around me whose MPXs ran were running hot or factory ammunition. The MPX at 150PF is flatter and softer than the best tuned AR9 at 130 PF. It is just a function of their designs. I have gone back to stouter loads and my problems have gone away. I will say I have not heard of anybody having reliability issues with the Gen 3s but they haven't been out long enough for a large sample to have a significant number of rounds through them. The Sig cleaning is more involved and if you put a decent number of rounds through them you will need to replace gas rings, extractors and springs much as you would with an AR. Many will also want to change the trigger and the stock. Some are okay with them though.
The JP is the energizer bunny. It just keeps running. It is utterly reliable other than an occasional firing pin breakage but the carbine still works fine even with it broken. You will just find it when you are cleaning the gun. the JP is noticeably heavier and more specifically feels more nose heavy to me. The handguard while feeling, great carries a lot of weight. You can tune these to shoot pretty flat and there seem to be a couple of options on how to do that. The trigger on the JP is light years ahead of the Sig. The Sig Gen 3 has a 4 1/2 lb Timney trigger that I found heavy and did not like at all. The regular JP trigger is probably a little over 2 - 2 1/2 lbs and has a great break to it. On the flip side, I think the MPX magazines, while far more expensive than Glock mags, are also much better suited to running 40 plus round magazines. If you are happy with a 33 round magazine this would be a non-issue.
In the end, they are both great choices. At this point I would say the JP has the proven reliability record as the Gen 3 MPXs are still new to market. The JP is easier to service and all you would need to do if you bought one would be to put an optic on it. All that said, I have both in the safe but for our local match tomorrow I am definitely bringing the Sig. If this was a major match that I was traveling to...... I would grab the JP. I am interested to see how the Gen 3s hold up though!
I hope this helps some and of course, it is just one man's opinion.