I'm expecting you to get a very heavily-biased "pro Pacifica" response here, so I'll try and give you a more rounded response: yes you will encounter more problems than with a new 2016/17 Odyssey (or Sienna), for two reasons:
1. This is a brand new car; Chrysler will only learn and fix problems at-scale as more people buy these and bring them in year after year for warranty repair. This is true across any manufacturer even the Toyota's and Honda's of the world.
2. FCA has a well-know reputation for quality problems. You can find infinite number of people that have "absolutely no problems" with their Chrysler and an infinite number that thought "it was the worst car they ever owned" - ignoring the individual stories and just looking at overall trends and reputations, chances are very good you will have more problems with your FCA vehicle than you will with a Toyota or Honda.
To Point #1 above; every subsequent model year of a car that hasn't been drastically changed typically gets more and more reliable as the manufacturer is able to fix known issues... the Honda Odyssey is currently in it's last year of the 4th Generation... that is a lot of refinement.
The only (important) thing I think you give up by going with the Odyssey is the autonomous driving capabilities that won't be in the van until 2018 (just announced this week). If those aren't important to you, by all means, get an Odyssey.
If those are important to you and you can wait until April/May, the new 2018 Odyssey will be on dealer lots and you can cross-shop the two vans.
I come off pretty prejudice here so why am I on a Pacifica forum?
Because I own an FCA vehicle (and Hondas), I enjoy the FCA styling more, I love the utility of the Stow and Go seats, I like that I can get a better deal at a Chrysler dealership when buying a new car and some for some stupid reason I feel drawn to the FCA fleet of cars more than others even though I've had my own challenges with my Dodge.
There is an intangible draw I think some vehicles have for people and the Pacifica does that for me; it's an awesome van and plenty of owners don't run into any problems at all, but many do and I'll say with 100% confidence that your ODDS of having problems are higher; that doesn't mean you will though.
The buggiest thing in the vans right now are the UConnect Theater system... it's a $2700 option; if you can just buy your kids all iPads and forget that feature, you'll avoid a lot of the heartache people are having.
One last thing (for what it's worth)... Consumer Reports predicts worse reliability with the Pacifica than most other minivans... BUT it currently has the highest Customer Satisfaction rating of all the minivans they test... so you aren't crazy for shopping for one, they are great vans.
Hope that helped. Just optimize for your "needs"... if you can never have the van in the shop and don't care about autonomous driving (which also means auto-braking/crash avoidance) then get the 2017 Odyssey.
If you can wait a few months, wait until the 2018 Odyssey is on lots and cross-shop/test-drive it.
If you don't care and really want that new van this Saturday (this is a totally valid reason; I've bought cars for no other reason than I was bored before) then go for it.
If you do buy it this saturday, I would recommend you go through the PROBLEMS forum and get a list of things that most people complain about it and test each one on this van.