So many people have made such very good points. I'll just add a few of my personal experiences and observations from having owned 13 boats over 43 years of boating.
10 of the boats I've owned have been bought used, 3 were new. As others have wisely said, there is no simple, absolute answer of "new" vs. "used" being "better". It really is a complex eqaution that totally depends on what you are looking for, what kind of boat will suit your needs, what kind of boating you plan to do, your willingness/tolerance/patience for problems and doing maintenance, etc. A boat to do true blue-water long distance cruising will differ greatly from one which will spend most of the time at the dock as a floating weekend condo. The one fixed variable in your equation seems to be price (as it usually is for most of us...), so that will dictate much. As Sunchaser said, if you want something in the 42-46 ft range, it doesn't exist new in that price range (and if it did, you wouldn't want it). $350k will buy you anything from a new 34 ft American Tug to a used 53 ft Hatteras to a new 27 ft Hinckley to a used 49 ft DeFever or a 55 ft Sea Ray - all of which are very different boats for very different purposes, and not interchangeable except for what they cost.
I completely agree with ScottieDavis's comment of buying the smallest boat that fits your needs and for your budget - which is the opposite of what many people do. Do you plan to actually go cruising and use the boat? So many people have commented that the smaller the boat, the more you use it. Will it be a floating weekend home that rarely will leave the dock? Then the bigger the better it might serve your needs.
Many people buy the very biggest boat they can for their budget, and end up sacrificing reliability, seaworthiness, and construction quality. They often end up unhappy, getting little use out of the boat, and also often end up pouring a lot of money into it trying to get it into shape.
This happened a few years ago with a friend of mine. He bought the biggest boat he could find for his $250k budget - which was over 20 years old at the time and not in the best condition. Over the next 5 years he ended up pouring almost $500k into it for one repair after another (first one engine, then the other, then one transmission, then the other, generator, rewiring electrical system, air conditioning system, fiberglass work, on and on, good money chasing after bad). The boat today might be worth half of what he originally paid for it, and despite all the work, he rarely leaves the dock out of fear that something else will break.
My own personal philosophy is to trade size for quality. Quality in terms of construction, reliability, seaworthiness. This wouldn't work if you are looking for a liveaboard, or need a certain minimum size to accomodate a set number of people. But, having owned a range of boats from "quality" to "price leaders", I've always been much happier with the quality boats. They have caused far fewer headaches, and let me have more time out on the water. They also hold their value better. I bought a 2001 34 ft American Tug new, and 4 trouble-free years later, sold it for exactly the same price I paid for it.
When I started out looking 3 years ago for my current boat, I was absolutely certain I was going to buy used. It was and still is a buyer's market, and I was tempted by the siren song of all of those ads on yachtworld, and had dreams of getting a bargain. They do exist out there, but my own personal experiences were that it was a lot harder that I thought.
I literally looked at over 100 boats in 3 years, and surveyed 24 of them. I was appalled at the junk that I found out there. So many of the boats that I saw, even in the $300-$400k price range, were just junk. 23 out of 24 boats I surveyed had significant water intrusion into the core, which is a deal breaker for me (and the only one which was dry, the seller wouldn't budge off a price for a 10 year old boat which was the same as a new one). Like with anything else that is advertised for sale, there were huge differences between the yachtworld ads and broker's descriptions, and what I actually saw.
I was also struck by how inflexible so many sellers were. While there are sellers who eventually get a dose of reality and lower their price to what the market will really bear, I found so many that, despite their boats being listed on yeachtworld for literally years (7 years in one case!), would just not budge off their prices. Sometimes this was for financial reasons, they owed that much on the boat and couldn't take a loss, other times for emotional reasons.
The bottom line of my own experiences was, after 3 years of looking at over 100 boats, I ended up buying a new one. This worked for me, for the kind of boat I was looking for and what I could get in terms of size for my budget, but your own situation will be unique to you. Even if you decide to buy something new, don't assume that just because it is 'new' means it's the right boat for you, or good quality - I've seen some scary things in the nooks and crannies of some new boats, in the dark, cramped places where most people don't go, that have scared me off of some brands!
If you think you'll own the boat for about 10 years or so, focus on what kind of boat will maximize your enjoyment over that time. After 10 years, the condition of the boat and the upkeep you give it will likely have a more significant impact on its resale value at the time than perhaps the make, and repair and maintenance costs over a decade of time will likely be a significant fraction of the original purchase price anyway. Like ScottieDavis suggested, figure out what kind of boat will really suit your needs for the kind of boating you're going to do, then buy the smallest, best built, best condition boat (whether used or new) that will meet your needs.
Then get out on the water and enjoy yourself. Life is short, and there are no do-overs. You've still got most of this season left!