What is ideal for long distance road bike rides 23mm or 25mm tires?
A 25mm tyre can be run at a lower pressure with the same rolling resistance, thus giving you a slightly more comfortable ride, and slightly better grip in wet conditions or on a dirty surface.  If you take that reduction in pressure too far, you'll get more pinch flats, but you'll be very comfortable just before you stop to fix that flat. :-)

However, if you inflate to the appropriate pressure then you'll get a better ride, better grip, with minimal difference in rolling resistance - the downside being weight, and possibly an increase in frontal area causing a little more drag.    So why don't the pro teams use a 25mm if there are all those advantages?  There's some indication that they have been starting to over the last few years: 


http://www.cyclingweekly.co.uk/news/latest-news/are-wider-tyres-really-faster-160403
http://www.competitivecyclist.com/learn/25-vs-23
http://velonews.competitor.com/2012/05/news/giro-tech-rise-of-the-25c-tire_218011
http://cyclingtips.com.au/2014/04/tyre-trends-what-the-teams-are-using-for-paris-roubaix/


So what is the right pressure? Here's how to work it out: a 25mm tyre is about 8.7% wider than a 23mm, so round that to 10% for easier calculations which means that you can run about 10% less air pressure in a 25mm as compared to a 23mm.  E.g. if you typically run a 23mm at 100PSI, then run your 25mm at 90PSI.

Note - I have never had a pinch flat in a road tyre in 15 years of riding road bikes, so if that is your concern, the you may be running your tyres at too low pressure for your weight (or your local roads are much rougher than mine).  The thing about the weight is not meant to be an insult - I'm just reminding you that your tyre pressure needs to be in proportion with the weight that's being supported: made up of your bike, you, and your luggage.

If you're riding on gravel/dirt often, consider a 28mm - but first check that it will fit in your frame (1 of my bikes can fit a 28mm on the front, but only a 25mm on the back - which is a bit annoying).