I live in Groton (in case you didn't catch that from the name

) and I can honestly say that although Groton and New London are very close together, there is not as much cross river activity happening as one might expect. The feel of both cities is quite different from one another. New London is a vibrant, more art centered city, with many entertainment spots, as well as being more urban minded in their approach to zoning and development. Many great new revitalization projects are underway in the middle of downtown that are making it a significantly more attractive place to live and work, and that is a very welcome sight here in SE CT.
Groton, on the other side of the river, is much more industry and commerce oriented. While it is significantly more populated than New London, it also covers a much greater area and is very suburban oriented in it's zoning and development; however the City of Groton subdivision highlighted in their most recently adopted plan of conservation and development, plans to refocus their development efforts into more urbanized development. There are not as many established entertainment and dining establishments in Groton, however there are more parks, more places of employment with higher median salaries, and a greater emphasis on historical education.
The economy in the two cities are based on two main industries: Defense and pharmaceuticals. The US Navy Submarine base, General Dynamics Electric boat division and a huge Pfizer campus in Groton, and the US Coast Guard Academy, and Pfizer's global R&D headquarters in New London anchor the economy here along with the two major casino's a couple of miles north of here that do much for tourism.
When it comes down to it, it is a matter of personal taste, if you are a young person or couple I would suggest New London, if you are looking more for a suburban feel while still remaining affordable and retaining the amenities, I would suggest Groton. Also while you are here this weekend, I would suggest checking out a few of the surrounding towns such as Waterford, Ledyard, Stonington, and East lyme. I hope you enjoy your visit and like the area!