I play in Franchise 98% of the time. I enjoy the trading, breeding, and care of the animals. I take part in many of the community challenges as well.
I also play it as a true franchise, meaning that I transfer animals between my franchise zoos, and manage their genetic diversity over generations. So it's not merely that I have a single zoo that happens to use franchise mode rules, but more like I am being a tycoon or running a collection of zoos (like the AZA, EAZA, ZAA, etc.), and my animals are part of a regional collection plan for me to manage long-term. Whenever we get new animals from a dlc -- or even a new color variation like albino, melanistic, erythristic, etc.,-- I kind of treat it as if the regional organization has adopted a new SSP (Species Survival Plan), EEP (EAZA Ex-situ Program) or SMP (Species Management Program).
I tried sandbox briefly, but got bored of it pretty quickly. All of the things that other people wanted to turn off in the name of creative freedom, I wanted to leave on because I'd come to think of them as creative challenges! And because the franchise market and community challenges are always turned off and unavailable in sandbox, I found that the entire side of the game that involves animal management, stats, genealogies, and breeding of animals lost their importance to me in sandbox, because no matter how well I took care of them, they were stuck at the absurdly under-priced base prices that we start with as beginners. So basically, all of the things that sandbox players say they hate when they try franchise after living in a sandbox world for a long time, I find that I miss when I visit sandbox world.