Hire vs own. Well, if you decide to purchase everything on your own, 100% of the costs of the gear, labor and any maintenance of that gear are on you. You're now responsible for hiring the staff, ordering replacement parts, etc, etc. If this is not a full time tour, where you can pay someone a full time wage, hiring reliable staff is going to be a nightmare that you're not going to want to deal with.
If you work with a production company, or multiple production companies, then all you'll need to do is tell them what you want and when and where you want it. Now it's on them to source the gear and staff to make it work. If a company isn't working out for you, then you find another one.
When you hire a production company that also does other jobs, that means that the expenses of gear and back end work can get spread across multiple clients vs you having to fend for yourself. When your tour ends, the production company then continues on doing jobs for other customers to recoup the gear costs. If you buy it on your own and your tour ends early, now you're still on the hook for the gear. Resale value of used tour gear tends to be very disappointing.
Now, if you're working with multiple production companies, sometimes there are particular pieces of gear that are important to you that can't be rented. ie, if you like a particular type of microphone, maybe buy that so that no matter the production company, your mic is always the same. If you can keep the amount of stuff that you bring along in the size of carry-on luggage, you can more easily travel across the country vs if you've got to get a truckload of stuff a 30 hour drive away in 12 hours.