Verizon DSL → Will Verizon 15 mbps ADSL2 work as well as 3 mbps ADSL did?

I had 3mbps Verizon DSL a few years ago and had good line quality stats (enough to get provisioned for 3 mbps), and I routinely got 2.7-2.9 mpbs download speeds in speedtests. If I get the ADSL2 package with speeds of up to 15mbps, is it safe to assume I'll see speeds of over 10 mbps, and perhaps even up to 13 mbps ((2.7/3) * 15), or is ADSL2 much more sensitive to distance and line quality?

No, it does not work like that. First of all, for a given distance from the DSLAM (which basically determines line attenuation), ADSL2 is never slower than ADSL, but it is faster the closer you are to the DSLAM. For 13 mbps you'll need to not be more than a mile or so away. If you are around 2.5 miles from the DSLAM or more, ADSL2 and ADSL are about the same.
What were your line statistics (attenuation) before? That should give a pretty good clue, assuming you will be connected to the same DSLAM location.

I'm about 1200-1500 feet away, and I don't have the statistics offhand because it was a few years ago, but they were very good.

Also, something I'm curious about is whether Verizon (in NY) is even committed to providing local phone/DSL service anymore. Can I expect bad service from them, and if so, should I avoid them and go with something else (like cable) if I have a choice?

since you have no stats, then the only real way to tell is to try and see what happens. if you really are the 1500 feet away that you say you are, then 15 is more than doable, heck, you might even be able to do 24 (max adsl2+ limit) if verizon offered it. this all does rely on having a good quality line though.

as far as them being committed to providing service, i wouldn't know that either, but i assume that you should be able to get it.

Thanks for the help guys.