Hello Mark,
As a competent tower and whilst the caravan is connected to the tow vehicle, then you should find no practical difference in how easy the SA or TA caravans tow.
You will notice a difference in the feel of the tow, as the TA trailer rides differently over bumps and dips, A correctly loaded single axle caravan will always have a positive nose weight which under dynamic towing will always keep a substantial part of the load on the tow ball, but a TA will develop a rocking motion each axle rides the obstacle. You can feel this in the tow vehicle. If you get caravan loading wrong, the nose load can become negative at times, and this can feel disconcerting and with worn couplings there is a risk of uncoupling. For this reason nose loads are important.
The TA layout definitely affects the off-vehicle manoeuvrability. If you have a tight parking spot, you may need to consider some kind of caravan mover.
The jury is still out about the additional 'tram lining' effect that you might expect with a TA. Does it impart any greater resistance to side winds and overtaking, some say yes some say no.