We are doing nutra on FB and not really using the FB pixel (not risking it at this point but looking to get that done in the future).
What option would be the best for us to select?
Conversions (cpm) OR Link clicks to your website (cpc)?
If we go by data history, our campaigns have always performed the best on native using cpc by a long shot.
Looking for suggestions, thx!
Well, I wouldn't compare bidding modes on any traffic source to Facebook. The fact is their bidding likely uses a completely different auction model and is a lot more complex in the parameters involved.
First off, split your focus here into two parameters - it's important to understand these for Facebook:
1. The ad delivery optimisation setting - this is set at the ad set level and determines the type of user your ads will be preferentially delivered toward in your target audience. The options you can pick here depend on the parent campaign's objective. The campaign objective itself means little - focus on this ad set level setting.
2. The bid mode - depending on #1 you may be able to chose CPC, average bid, maximum bid, auto bid, etc. which then charge on a CPM basis.
So, my first suggestion is to focus on split-testing your ad delivery objective, i.e. conversions or link clicks. This will alter the audience and this will affect performance the most - i.e. test clickers vs converters, the trigger happy vs the ones known to convert on site.
I would keep bid mode the same - i.e. CPM, either on Auto or with a guessed manual (average) bid.
To do this, you'll need to make a campaign with objective of website conversions, to test converters + average bid mode (e.g. $30) + CPM charge; you'll then need to make a clicks to website objective campaign to do link clicks as the ad delivery optimisation setting + CPM charge mode + a manual bid of "what a click is worth to you" (e.g. $3).
In either case you could use Auto instead, which is probably a fairer test.
Confusing? Good, FB is confusing. The nuance here is that if you make a campaign with website conversions as the objective, at the ad set level you can choose link clicks as the target optimisation type, but you can't then be charge on a CPM basis so it makes things less fair to test -- hence the need for separate campaigns.
Anyway, I would first test this and get a feel for what ad delivery segments (i.e. converters vs clickers) are actually backing out better for you. You don't strictly need the FB pixel in order to use the conversions objective, though you will fail to leverage FB's modelling systems well here (you will waste money for sure) which is combined with the converters segment/auction being the most expensive to work with.
Once you have tested that, try out CPM vs CPC and different bidding variations. These will matter less than who you are delivering to - at the end of the day Facebook wants to maximise their EPM so bidding CPC vs CPM is unlikely to give a huge difference (it all gets normalised in the auction process anyway, really, so any subtle differences are likely to even out at high spend).
Craziness ... got more than expected here, haha.
Now I gotta digest all of this.
Thanks for all the info, gonna print this out 
"Confusing? Good, FB is confusing. The nuance here is that if you make a campaign with website conversions as the objective, at the ad set level you can choose link clicks as the target optimisation type, but you can't then be charge on a CPM basis so it makes things less fair to test -- hence the need for separate campaigns."
Yo Zeno , if you use Qwaya you can do WC => link click then impression FYI
Perhaps, would have to check, often you can force things through the API, though I think people often misunderstand the point of it all (with regards to the campaign objectives and so on).
If you make an ad set and you choose to optimise toward link clicks - as the target optimisation type - then this determined delivery regardless of whatever your campaign objective is. So having this inside a WC or WC or PE etc. campaign is irrelevant.
To put things simply, your campaign settings don't mean much. Your ad set settings do.
I just used it to test ;-) but yeah you are right , was just FYI