
Here are some differences that might make your DW transfer easier. I've been on this website for about 7 years now, and although I'd been using it before as an RP hub as a refugee from LJ, I figure some people might not have that experience.
Tags
Tags are organizational only, unlike tumblr. There are no global tags; if you want to show up if someone searches a fandom, you have to put it one of your interests on your profile. For that matter it's generally considered bad form to have tags as commentary--it clutters your tag list and makes organization harder.
Privacy settings
You can have all of your posts under an access-only filter, but this is opt-in. Granting someone access means that they have access to that general filter, but you can create additional filters which you manually add people in your circle to opt in. This is nice because you can basically tailor your blog experience for other people, but the additional opt-in filters are something I'm not 100% confident with yet. :P
Communities
They're basically themed blogs run by all the members of that community where anyone in it can post. Chances are you knew that if you saw me on add me, but it's worth mentioning anyway. Some groups require you to request to join them so they can approve it, and you may be locked out of entries until you get approved.
General etiquette
DW is a slower platform than tumblr, which is something we're going to have to get used to, but it's encouraged to interact and leave comments. There isn't any equivalent of a like, so commenting is the only way you can interact with a person's content. You can also share other people's posts on your own by directly linking them the old fashioned way (of course ask permission) and generally that's used for prompt calls, kinkmeme prompt calls, or other events you want to draw attention to.
Dreamwidth Points and Paid Accounts
DW is a free service and it's really nice that they offer pretty comprehensive service for free. But with a paid account, you get either 100 icons, more image storage space, more sticky posts, and other perks that make it even better. If you have the means, I would honestly recommend supporting DW staff--they're pretty great. Also, in December you get extra points when you buy an amount! Something like 10% of your tot purchase I think.
If you do want to get a paid account (or pay for extra avatars $1 at a time) you need to first buy the points and then apply it to your own account, because you can (and people often do) buy paid time for other people. There's even a community dedicated to people asking for paid time. (God help me if I can remember the name of it right now.)
Customization & Sticky posts
DW offers a lot of themes to chose from, and you can also edit the skin of the website itself when you view it. You can also go to your blog settings and set sticky posts (that is, posts that appear at the top of your blog) by copy and pasting the url of the entry you want to sticky. By default, free accounts get two sticky posts. I find they're useful for directories, abouts, linking other places (like I did), or letting people know your privacy settings (if you're an access-only account you can set it so that sticky is viewable to everyone but the rest of your blog is locked automatically.)
That's what I have right now, but I may add to this in the near future when I think of more stuff.