Hoping a new Macbook Pro model comes out soon...
Generally, when we've hosted traveling VJs, they have the max-ed out Macbook Pros and they work quite well and consistently, especially if you're pushing a 1920x1080 texture (they do get finnicky when you're pushing more than about 2 layers at 3840x2160, however). I know AMD cards don't always cooperate so well with Arena on PC, but on Macs they are much more stable.
I cannot really speak to their handling of multiple outputs, but I have read on this forum from a few folks that using Blackmagic capture devices (such as an Intensity shuttle or a Decklink card inside a PCIe over Thunderbolt chassis) are solid options.
I am in a similar position — I know that the real work I want to make requires a PC tower, and I'm working on it, but I really need a portable solution. For the sake of saving money and being able to customize with maybe something like NVIDIA GTX970m, I would want a PC notebook, but all the custom builds look/feel way too "gamer" for my tastes, some of them are rather bulky too.
TL;DR - if you need an Apple machine, getting the most tricked out Macbook Pro is your safest bet. PC has the potential to perform even better, for cheaper, but requires more purpose-driven research.