Once you have your shoulders relaxed with a good embrace, and your hips in the right position to support your back, Argentine Tango should be a lot easier to manage for people coming to it from ballroom dancing. There's really only one thing more that people complain about: "My feet hurt!"
A lot of ballroom teachers teach dancers to get up on the balls of the feet to dance. Although I personally would never counsel that having been a student of anatomy and kinesiology, I can see that the "look" of the dance is being stressed over the "feel" of the dance; I understand even if I disagree.
What's different in tango?
Tango requires a constant preparedness to change direction. As it is much more improvisational, neither the leader nor the follower may have a plan further ahead than the current step in many cases. Balance and ability to pivot and change direction take precedence over everything else in terms of the foot.
More surface area improves balance
Get those heels down! Spread out your toes! Yoga talks about the four corners of the foot: use that concept in tango.
Think about elephant feet: elephants have good balance and REALLY big feet. Imagine you have huge feet that hold you up. If you are in heels, pretend that teeny stiletto heel is enormous!
Engage your arch for pivoting
This is especially true for turns. Instead of popping up to remove as much of your foot as possible from the ground, stay more grounded. You need to keep your metatarsal arches as the center of your work, so spread your toes out, rather than scrunching them in. Yes, it takes effort to keep the arches as the focus, not the heads of the metatarsal bones. However, using that arch for support means more hours of dancing before your feet give out.
Build your ankle strength
I inherited very weak ankles from my mother. I was always the kid with an Ace bandage from spraining and straining my ankles. Luckily, seven years of West African dance training coincided with my Argentine Tango beginnings. That helped a lot, but I still didn't have the strength to work correctly in high heels
I have worked hard to correct that, and have used ankle exercises based on the ones that I have learned from physical therapists and trainers to help my students also build their ankles. A lot of power in tango comes from the foot and ankle working together. Once the ankle is strong, the temptation to take all of the work into the toes, ballet-style, can fade :-)