Both work, actually. I do both pretty regularly, and bring the money on JV deals and split profits too.
Here's what so many people miss with this "its cheaper to borrow" stuff, once you get to 100% financing its more about a return on time than anything else. Just do bigger and/or more deals to cover the split difference. Plus, once you get to 100% financing with someone else running your rehabs, guess how nice your life can be?
Finding them and funding them is where you should be spending your time once you know what you're doing, that's the part you can't really outsource. The rest of it you can pay someone else to do for you. If you can get them funded at 100% with minimal supervision you can up the size of the deal and up the volume without much additional work. I'm running 9 right now, well 6 active, 3 are newly on the market. I might have put in 3 hours of work today. Don't get me wrong, I have my 17-18 hour days too, but I'm not exactly overwhelmed with those numbers and I have zero of my dollars in any of them.
Jeff is spot on, in this environment, the deals are harder to come by than the cash. In most markets, anyway. It was the opposite in 2012.
On the split stuff, I personally don't do them when I bring the money unless the split is 50/50 and the profit is over $50k. Borrowing I pay my institutional lender (who I broker for) 2pts and 8%. I pay my private lender 2pts and 12%, but no payments there and he lets me put 2nds behind the institutional stuff if I want. I'm about 70% private money and 30% institutional money right now, its more expensive, but way less headache once the relationship is there. I could probably borrow for less, but I like to keep him happy so he says "sure" when I ask if I can borrow $360k by Friday on a Wednesday (I literally asked my guy that on the way back from a bar 3 months ago...got the money, bought the house and filed the security deed a month or so after. This is very much a relationship business)
Anyway, my advice is to go to the money guy and say you want to do business together but you are looking to structure it more for as a lender than a partner. You want to be the one picking paint colors and at what price to sell it at and you don't want to have to worry if you buy tools at Home Depot and bill it to the rehab, which is fine with a lender, but theft with a partner, etc. Also explain that it'll keep your relationship better, because there will be cost overruns and surprises and as a lender, his return is unaffected. Say something like "is there a rate of return that'd you'd be real happy with knowing the loan is secured by real estate at 70% of its value?" Mention the stock market is losing $ right now, then offer 2&12 or whatever.
Happy to talk you through what I do if you want to ring me up sometime.