As mentioned in previous posts, it's going to be hard for you to go wrong either way. I am going into my third summer with a
BX1500, and have no regrets. My two main uses are mowing and snow clearing, with a bunch of random other things thrown in.
The big BX decision is really to BH or not to BH. By looking at the 1850 and 1500, you've already decided the BH is not a big deal, or unaffordable. I must admit, though, that after reading about the Woods BH on a 1500 (maybe a year ago on TBN), I felt even better about not having a factory BH available. I doubt I'll ever buy a BH, but I like knowing I could.
When I was looking, I was debating between the 1500 and the 1800 (the 1830 and 1850 didn't exist back then). The differences were/are a little horsepower, and a little size (both in length and ground clearance). The height could in theory matter with regard to 3PH attachments (PHDs come to mind), but it's hard to get worked up over, and if you ever run into the problem, there are several ways around it.
Basically, I chose the 1500 because the differences didn't matter to me, and it was cheaper. The option of moving up to a BH-capable machine was too much, and very hard for me to justify. I'm sure I would be just as happy now had I bought an 1800, but I'd be a little poorer. I'm not sure I'd be any happier, though.
And, if you save a little money on the 1500 over the 1850, you can buy another attachment...