I bought a pair of 177 Mantras recently. Before buying, I tried last year's 184 Mantra, and this year's 177 Mantra and 176 Gotama, as well as the 183 Katana and last year's 174 Snoop Daddy. You're not asking about the Katana or Snoop, so I won't talk about them.
I weigh around 145 lbs and stand 5'8". I ski everything but park, with an emphasis on off-piste, especially gullies and trees, and not a lot of time spent in the air.
For me, the 184 Mantra was a lot of ski, but not so much I couldn't ski it from when I rented it through the end of the day. When I was skiing aggressively down the mountain, it was a lot to handle, but a lot of fun. In soft snow I occasionally had a little trouble keeping both skis doing the same thing. Going more slowly, for example on traverses, I got some speed wobble.
I love my 177 Mantras. It's still a lot of ski, but it does what I want it to and the only condition I've found where I have trouble is hard moguls, which I'm not really good at anyway. It skis with a lot of authority in softer moguls and can feel slightly heavy, but it's stable enough that I didn't really get nervous hitting the occasional bump straight on and catching a little bit of air. It also makes landing from a larger air feel a lot more stable. Going slowly, I can get them to turn but they're happier going faster.
I didn't like the Gotama as much. The day I tried the 177 Mantras and the Gotamas was a few days after a fresh snow day, but there had been a little bit of rain the morning before, so there was a lot of crud around. The Mantra makes the mountain ski smoother. The Gotama is livelier and felt a little bit turnier to me, and I found it a little easier to initiate turns, but it got kicked around a lot by crud, which really turned me off. That day, I did two runs on each ski: a groomer run and an off-piste run that had some crud-over-hardpack and some soft patches.
I think if I were you, I'd get the 184 - it was only a little too much for me, and you're bigger than I am.