I’ve been a max user since 2006, when i first got an educational version of Max 8, am currently on a student liscense of max 2012, which expires in July, so I too need to upgrade/switch programs, and since Autodesk does not allow the student versions of it’s software to be used for anything like game asset creation, I have no choice but to switch.
Personally, i’ve found modelling in max pretty easy to do, but from what i’ve heard, rigging and animating in Maya is easier with HumanIK for biped characters (unless you can get your hands on Motionbuilder, in which chase, you do all your animation in that), though i’m not really much of an animator (last time i did anything with a rig, it was a long time ago in collage, and was pretty crappy). The ONLY two things max has over maya is the CAT rigging system (which has full support for custom rigs and non-bipedal characters) and it’s material editor. I’ve always hated Maya’s Material editor, i don’t know why, i just never liked the look of it.
If pricing is an issue, then your only option (if you want to avoid the nightmare that is blender), is Maya LT, it’s about 1/4 the price of full maya, and is more specifically geared towards game devs (no simulation stuff, renderer or plugin support), the 2015 release will add in Mel scripting support and fix a few things they broke in 2014, and hopefully they’ll add python support in either an extension or the 2016 release (which should contain anything that was added in a 2015 extension). Hopefully they’ll also ad a “Send to Unreal” feature, like 2015’s “Send to Unity”, which allows for unlimited poly count FBX export directly into Unity projects, though i suppose there would be nothing stopping you from then just copying those FBX files into Unreal.
I would recommend AVOIDING the Rental License plans (the monthly, 3-monthly and yearly payment plans), as they will be more expensive in the long run (especially if you don’t go with Maya LT, full maya and Max are $200 a month for the basic rental plan), and if you stop paying them, You will LOSE access to the software, whereas, if you just pay for a yearly subscription, it’ll cost you less to stay up to date, and if you don’t renew it, you still get to keep the software at what ever version you’re at when the sub ends.
Be advised, that on February the 5th next year (or is it the 1st?) Autodesk will STOP providing Upgrade plans, so your only option then if you have a prior version and want to upgrade will be either get a full license plus subscription, or go the rental route.
Of course, if you’re on perpectual licenses for either software, then there is always the free FBX converter provided by Autodesk, and the latest FBX update for Maya 2012 should bring it up-to-date enough for it to work seamlessly with Unreal.