The parking lots aren't that much further... maybe 5min tops drive time. (compared to the 20min you could spend on the monorail between EPCOT and the TTC).
Personally, I'd consider parking at the TTC in the Morning and then hopping in the car and driving to EPCOT when you are ready to park hop.
Alternatively you could park at the TTC, Monorail to the MK, then Monorail from the MK to EPCOT that evening, Followed by another Monorail back to the TTC when you leave EPCOT.
OR do the park at EPCOT, Monorail to the MK in the morning, and then Monorail back to EPCOT when you hop.
Ultimately, I'd say there isn't really one easy one-size-fits-all "Best" option. I personally prefer to drive when I hop. It's often quicker, and my car is always at the park I'm at so I don't have to worry about extended transportation time in the morning or when I'm ready to go at the end of the day. I can also use my car to store items so I don't have to carry them all day thru both parks.
When I have a stroller however, The equation and considerations can change dramatically. I've personally found that the EPCOT parking lot size and design makes it much easier to walk from my car to the front of the park most of the time. No having to worry about emptying the stroller and collapsing it to fit it on a parking lot tram. The Monorail also allows me to ride with the stroller opened, so all the park supplies/toys/kid/etc can ride in the stroller in the monorail, again, without needing to empty or collapse it to fit it back in the car or on a bus or parking lot tram.
The monorails can also take longer to go between the parks..... and can be subject to breakdowns or delays.... so it's a game of weighing the pros and cons and figuring out what level of risk and/or time/effort is worth it for you.
