1. Much more comfortable (wider seats, more luggage space, etc)
2. A lot more convenient. No taking off shoes, check points and lines. Plus the chances are a train station would be a lot closer to the center of the city, rather than an airport.
3. Cheaper and less pollution.
E.g. If the CA High Speed Rail got build, it would take about 2.5 hrs. from downtown SF, to downtown LA. By plane it is about 50mins. BUT, you should add the time it takes for check in check out (at least 45mins), then the time to travel to the airport themselves (30 mins with Bart, if you live in SF), etc. If High Speed Rail would have been implemented throughout most of the major cities of US, It just wouldn't make sense to fly for short and medium distances. Coast to Coast, yes, coast to Midwest yes, SF to LA or LV, probably not.
I would imagine that the first part would change as rail became a more traveled medium, thus making it a more attractive target for terror attacks.
However, having train stations closer to the city centers than out in the suburbs would be great.
It turns out that high speed trains are a lot more robust than planes: the failure mode is usually "soft", i.e. the train comes to a halt safely and damage is confined to one carriage (unlike an airliner). To inflict mass casualties (e.g. 7/7, Madrid) attackers target either busy subway systems at rush hour (7/7) or busy transport terminals with lots of people (Madrid). It's worth noting that both 7/7 and the Madrid bombings involved large suicide teams and multiple bombs -- but killed fewer people than a typical airliner bombing.
But, there are may others relating to carbon footprint per tonne.km traveled, which have greater relevance.
China is building a national rail network running at 350km/h to with the goal of putting any city within an 8 hour travel radius of Beijing. http://www.globalissues.org/news/2010/09/30/7114
Kind of makes domestic air travel somewhat obsolete and really quite unnecessary.