Does the Hilton have bus service to the parks like the Disney resorts do?
Yes, all the DTD area hotels provide bus service to the parks. There are two buses, one for each side of the street. They're supposed to run every thirty minutes, and I've never had any serious problems with them. I will say that if your hotel is the last stop on the route, it may be a bit crowded for you in the mornings.
Now on to the initial question posed by the OP. I've stayed at the Hilton twice and at the Best Western once. Both are nice, and they both have their pros and cons. The Hilton was definitely more expensive, and you also have to pay a daily parking rate ($14/day, I believe). On the plus side, it's literally right across the street from DTD, and they have the EMH perk, if you're interested in it. The Best Western is further down the street from the Hilton and is on the opposite side of the street. You can still walk to DTD from there, but it's a bit more of a hike, especially if you're going in the summer. There's no fee to self-park, IIRC, and the overall price of staying there was definitely easier on the budget. Plus, I could see DTD from our room, which was pretty cool. I would definitely consider staying there again.
Since the OP asked for the nicest hotel, I have to say I think the Hilton is a nicer hotel, but I wouldn't hesitate to stay at the Best Western again, especially if budget was a concern. I haven't stayed at any of the other DTD hotels, so I can't comment on them.