Difference....opinion !

If you only do short hops the Sporty rig will be fine. The small Liberty Sport car is an obsolete sidecar (no longer produced) though cute it wasn't all that popular. The 1200 Sportster isn't as smooth as an 883 that has been converted to a 1200 due to higher performance cam timing. They tend to be less tractable for sidecar use as the lower performance motors since the 1200 is Harleys "Hot Rod".
Gas mileage is is also poor so unless you have extra fuel capacity you will be stopping for gas frequently.
Rider comfort with a solid mount Sporty also leaves much to be desired.
The Big Twin TLE combo is a touring outfit and has the wheelbase, tire sizes, weight, suspension and tractability needed for passenger and driver comfort on long touring trips or short range hops about town.
With moderate speeds you can expect over 40 MPG with a stock engine.
Either rig would benefit from raked trees for easy steering.

Lonnie

Hey Rod: I ride two rigs now: The K100RT EML double rig we just got up and running, and the 2002 883R with Texas Sidecar I've been driving for a couple of years. After 1100 miles over a couple of weekends on the BMW touring rig, this weekend I made a couple of day rides totaling less than 200 miles on the Sportster. Altho the EML touring rig is great for longer trips, I find I prefer the Sportster for local day rides, parades and such. The longest day on the Sportster was about 275 miles last fall, without issue. But as Hack'n points out, the smaller rigs do ride rougher that the heavier touring rigs.

My 2 cents: That as long as your hack rides are generally, but not always, within 100 miles of home with minimal freeway travel, a Sportster rig is not only adequate, but simply a lot a fun. However, if you desire to tour, such as 1000 mile 3-day weekends or 3000 mile weeks, the touring rig is the better choice. Or the Sportster hack for local rides coupled with a 2 wheeler touring bike.