This already exists
As an urban transportation nerd (side note, go follow Urban Planning Stack Exchange!) this is a big deal, and is the future of transit. The thing is, automated trains already exist and already work.
The Vancouver SkyTrain has 79.5 km of track and 53 stations. It has been in operation since 1985 and is fully automatic. For comparison, the Chicago 'L' system has 165 km of track and 145 stations; so Vancouver's system isn't tiny on the scale of things.
Automated trains are possible, work well, and are the future of mass transit. Go tell your local council-member, MP, or senator today.
There are many other systems out there, in addition to Vancouver's; via Wikipedia. That article talks about levels of operation: some subways are more automatic than others.
To answer the question more exactly, there are no differences in operating characteristics from human driven to automated trains. For example, the Red line in Washington DC last year shifted from human driven to Type II automation: computer driven with a human operator on board. There was no change in schedule, train length or train frequency.
There is no reason to want to shorten the trains. Trains do not have a relative advantage over cars until population and job density gets very high. There are only a few cities in the US for which an urban rail network makes sense: New York, Chicago, Boston, San Francsico, New York, Philadelphia, and Los Angeles. In other cities, the transit system would make sense only if efforts were made to increase either the population density in the downtown areas (Houston, Atlanta) or the jobs density (Dallas, Miami). Some cities have good downtown density, but just a bit too small (Minneapolis, Seattle, Denver).
Since urban rail is only an advantage to move large numbers of people in places where there is not enough room for cars, rail should concentrate on building to at least half capacity. The highest frequency subways in the world can get up to almost a train a minute through the busiest stations along the same line. NYC's 4/5/6 on the East Side runs about 49 trains, 8 cars long, per hour along the length of Manhattan during AM peak hours. Headways (time between trains at a station) are the limiting factor here.
If a rail system can't fill the tracks, then it can't make the money to pay for those tracks. Rail has high upfront capital costs and relatively high capital maintenance costs. If you drop cars from your trains, you are still limited on headways, even on automated systems. That means you are just dropping capacity and revenue.
The advantage of automated trains is in the labor costs. As I pointed out in the comments, for the MBTA in Boston, The FY15 Budget (slide 3) for was \$1.9 Billion, of which \$740 million, or about 39% was Labor costs. Based on the Boston Globe's breakdown of MBTA employees, around 40% of overall employees (bus and train) were drivers. Eliminating drivers could reasonably be expected to cut 20-30% off of operating costs for the trains. This would allow the shifting of more money to maintenance and expansion, and reduce the government's need to invest in the system, which would, of course, increase its political appeal.
Automated heavy rail the future of dense urban transit for cost based reasons. That challenge is to convince society, especially in America, to live in increasingly dense conditions to take advantage of this heavy rail future. If we can, there will be significant economic, equality and environmental advantages.