WordPress.com is nice because you don’t have to mess around with a server or, necessarily, with getting your own domain.
WordPress software is nice because you can do anything you want. Cue maniacal cackling off into the distance.
But more concrete comparisons:
The first thing you did was take out that little Meta toolbar on the side, right? It looks unprofessional and sloppy, though some people dislike it more than others (I hate it).
.com: go to your site/wp-admin or wordpress.com or someone’s site where they left up the Meta toolbar. It doesn’t matter which, since you can navigate the whole back end of WordPress after the one login.
Software: go to your site/wp/wp-admin. That’s pretty much the only option.
Themes govern most of how your blog appears. Themes are a collection of Cascading Style Sheets (CSS) that tell things to align left or align right or show up purple.
.com: There are a variety of free themes, and even more paid ones, and you can almost definitely find one you love. Typically from there you can also select background color or image and header image. If you buy an upgrade, you can also edit the CSS. You don’t get access to the CSS files themselves, though, so you are overwriting blind. If you are pretty confident, that’s fine, whatever. If you are mostly used to editing and not building and have never bothered to look at the source code for various pages, when WordPress updates and breaks your theme you will spend several hours drinking and frantically trying to correct the website, while text boxes float around seemingly arbitrarily and look completely different on the three screens you eventually end up looking through because you are trying to fix the header and you’ve changed the alignment and indent and mandatory margin but you don’t actually have access to the files and it doesn’t occur to you to override the vertical alignment, and you then switch to a different theme that is not actually broken but does truly horrifying things to your submenus. When you eventually wake up, vodka having beaten panic at about three-thirty in the morning, WordPress will have fixed it and you will spend the rest of the day in nihilistic despair.
Software: There are myriad themes and you can not only customize the background and header but also look at the CSS and pinpoint that this line of code here governs what color links default to and change just that to make everything violently orange. You will accidentally leave an extra space or digit or apostrophe somewhere and crash the server. Things will need to be reinstalled. You can take comfort in your own agency in the failure.
Seriously, though, themes and editing without messing with the CSS can get you a pretty customized website, and WordPress is great about fixing their mistakes and errors that crash the server can be corrected.
If you’re building a WordPress site, you freaking love widgets. Widgets are awesome. The Text widget (which lets you insert arbitrary text and HTML) is how you get your Twitter feed or follow button up, and your tumblr follow button, and a lot of the other buttons social networking sites let you generate. But widgets let you do a heck of a lot more than that: they’re your Facebook like box and your RSS feed and your contact info and your flickr link and your category cloud. Widgets are how you implement neat features without extensive background in coding.
.com: limited number, but they cover a lot, and the text widget with HTML adds additional functionality.
Software: widgets for the software are actually a feature of the plugins you can get. Plugins for the software are great, because you can get ones that tweet automatically every time you get a new post, or generate a new post every time you tweet, or do all manner of strange and unlikely things. The trick is that they are reviewed but not actively policed, so you need to make sure it actually does what it says it does, and isn’t broken.
Akismet is a spam filter, and is how you filter all the comments that are lists of links to scams or are soliciting people to buy knock-off Gucci handbags on your bike site. You want a spam filter. Akismet’s pretty good.
.com: it’s already there.
Software: you need to install the plugin. It is a terrible amount of work. You have to click, like, three things.
What do you do when you suddenly get lots of traffic on your website?
.com: It absorbs the traffic, and doesn’t cost you extra money.
Software: Your server might crash, or you might need more servers. This can cost more, and may or may not be able to respond quickly to a sudden surge.
Which you choose will depend on your comfort with code, your ability to acquire and comfort with self-hosting, and how much you like customizability. They’re both excellent platforms, versatile enough for almost everyone.