Service work can make more hourly wage, but the work and hours may not be consistent. New construction may be less hourly, but with a good company that has a lot of contracts, you could get your 40+ hours a week.
New construction makes it's money off of volume and low overhead and can turn into a rat-race resulting in poor quality of install. The benefit is that you can learn a lot of the code required for a license where service plumbers are not exposed to the code except in school.
As Mr David noted, new work is not in such a demand these days. Pickins' may be slim on both sides, since most new construction plumbers are turning to service to make up for the loss of work. It's a real gamble, to be honest.
Lately it has been rare to find hard working, dedicated, ethical plumbers and apprentices that are truly passionate about the trade. I am an employee, not a company owner, but I see a lot of guys who think that they will make $50 an hour changing faucets. There are a lot of myths related to plumbing and the best way to find out is to jump in, get your feet wet and find out if it is right for you.
I was running nursing/residential care homes before I became a plumber. It was on a whim to get away from the stresses related to the type of work. The managers and owner were taking bets as to how long I would last. One day?...one week?...one month?...the owner won. I'm still plumbing after 11 years and got my master's license 6 years ago. The soft hands and clean cut look fooled most of them, but it all depends on the individual.
So, like I said...jump in and get your feet wet!