I'd say the order depends on your family and your likes/desires/situation.
Assuming parks at both will be crowded, for Disney, that will usually mean someone will spend some time trying to plan out which park to do go to on which days. Then once you have the park order in mind, you then want to plan out your Fast Pass strategy. Which rides to get your initial set of FPs and don't forget you need to plan out when you can reserve those (60 or 30 days in advance). And then you will probably have to plan out your next round of FPs to grab once you use the initial for that day and so on. And in between, you probably will want to plan out exactly which rides you will hit in between. There are whole websites dedicated to minimize wait times for the Disney parks. With a lot of planning and sticking to that plan, one can usually minimize wait times to be able to hit the most rides in a day. And of course the more crowded the parks, the more it can help really planning out each day at Disney. And don't forget, if you really want to maximize rides with a minimum of line waiting, you will need to keep track of which park(s) has early entry (not sure if that has started up again yet, and my understanding is late hours will no longer be included). To maximize your stay, you will probably need to be there early to get into the park for those early hours (if you can). That means getting up really early (more so if you coming to Florida from the West coast.) So you will probably need to open and possibly close the park to really hit most everything in a day. That means long hours in the heat of summer. And if some of the little ones are getting a little grumpy, they might need a some "pushing" to get them through it. Over a number of days, this can be very tiring (i.e. chaotic as mentioned above.) Though there are those that really do thrive with this and love the planning, the thrill of making that plan work, etc.
At Universal, if you can get a night or more at one of the 3 Premier hotels (RPR, HRH, PBR), you will have unlimited EPs for the days around your stay. With those, you won't have to plan out anything concerning Express Passes as you have an unlimited supply for those days. You don't have to pre-plan months in advance which park on which days. You can wake up each day and decide which you want. You don't necessarily have to be there for early entry (though on really crowded days if you want to hit Hagrid's then it might be helpful and not sure if the Velocicoaster is open during any early hours.) But other than that, you could wake up and get to the parks at a more leisure pace while still being able to hit every ride you want (and possibly multiple times too.)
For me, I'd want to do the faster paced, more planning, have to be there early and stay longer Disney first. This allows us to have more energy to do those things. Then as our energy levels are lowered, we head to Universal second where we can probably still hit all the rides (due to having unlimited EPs) while being able to sleep in a bit and even leaving the parks a bit early to have some extra down-time at the pool. If you do this the other way, some while having to wait in longer lines, might get a little nostalgic remembering how quickly they were able to get from ride to ride with possibly much shorter lines.
With that in mind, I'll offer another suggestion. Pick Disney or Universal, not both. If money is no issue, then by all means, do both. But doing both parks in one trip will usually increase your costs. For the most part, park ticket prices go down on a 'per day' basis the more park days you pay for. This can also apply to hotel rooms plus you have to get transportation from one to the other. So instead of purchasing a 6 day Disney ticket and a 2 day Universal ticket, save that $270pp and add 2 extra days to your Disney tickets. Adding those 2 extra days may only cost $65pp saving you over $200pp. And don't forget, if you are changing hotels and parks in the middle of your vacation, that is half to a whole day lost just to pack-up, check-out, check-in, unpack. That could be time you could be laying out by the pool relaxing. And usually we will NOT rent a car which will save on the car rental and parking. We pick one and pretty much stay there for the duration and we've never yet got bored at either location. So I have rarely tried to do both Disney and Universal in a single trip. It adds to the cost and takes time away from the vacation. But, I will admit I'm "assuming" you will make it back to Orlando at some future point to hit the other parks.