Brendan, I almost sense a hint of desperation in your post. Don't forget that "best" like beauty is relative to the beholder, best for you might not be best for me.
In simple terms the Boxford scores on the size and rigidity side being larger capacity and more heavily built that the Myford. Typically that makes it better for larger, heavier work than the Myford. If you had to earn a living with this type of machine (you'd be hard pressed but if you did) using it for purely turning the Boxford would be better. It also scores on the value for money side, there are lots that have come from the educational world with little use and because it does not have the following of the Myford and is larger and heavier it is less popular. It's the typical market forces lots of machines/few buyers cheaper price. The Boxford (the *UD) models anyway pack all of this into a very small footprint.
Looking at the Myford it is much more of a general use machine capable of a bit of boring/milling as standard and with the gap bed can swing reasonable diameters as long as they are short. It is lighter and smaller than the Boxford and more easily moved by someone on there own. It has a tremendous range of accessories available to make it do almost anything within it's size range. As John S said it was much cheaper than the Boxford when it first appeared and ideal for those who could only afford one machine. it was very much the right machine at the right time at the right price. Difficult for other machines to overcome that advantage particulary when there are thousands available. So if you plan just one machine in a small workshop and would find a huge amount of "how to" articles helpful, the Myford is difficult to beat.
So depending on what you want the machine to do you need to choose the best for you. The other issue with this hobby is that a major factor in how successful you are in using a lathe is the feel of the machine. Whilst they can be used robot fashion (as in CNC) most people develop a degree of "feel" and empathy for their machine, they can sense when the cut is progressing well or when the machine is not happy. The feel of these two machines is entirely different and you really need to play with both and see which you are happier with. No one can tell you which will feel better to you. Obviously, anyone can get used to anything if they have to but if you are looking for the best machine for you that you want to enjoy using, it is a factor that you should research.
Having said all this, there is no doubt that if you want a lathe purely for turning and cost is a major factor, and room is not, then a good Boxford AUD/BUD is difficult to beat. If you want a lathe that will do a bit of boring/milling with a massive knowledge base available and cost is not the major factor, the Myford is hard to beat. An additional complication is that the Boxford can be made more flexible by changing the cross slide to a flat topped boring table, however that is an additional cost to the standard machine.
I don't know where you are based but if you get in the South Wales area you can come and look in my little shed, I have both. If we are all honest with you Brendan, either machine (together with some of the imports) will make a fine lathe for personal use. They are all capable, reliable and will introduce you to hours and hours of fun and frustration. As has been said before - you pays yer money!
Best regards
Keith