Filter Tag verses HTML Code

Better is what's best for your skill level.
The filter is available for folk who never want to see HTML, and whose image manipulation requirements are minimal. It's quicker, but less useful in the long run. Fine for write-once blogs, less so for magazine articles or designer sites.

I'm totally comfortable with HTML, and can type out an img tag faster than I can click through pop-ups, so I personally favour code, but wouldn't try to teach my clients to do so.

It's up to you, both choices are valid.

The inline filter tag inserts not only a caption, 2.x also comes with improved support for CCK fields in your image nodes as well as Token support to generate custom captions.
Other benefits of the inline tag:

- Staging: URLs are properly transformed when moving between servers, properly accounting for different site settings, such as base path.
- Tracking: Image Assist stores information which image is embedded where. Preventing removal of images that are in-use elsewhere is not yet implemented, but is possible.
- Updates: Already inserted images can be edited via Image Assist's wizard again. HTML is hard-coded markup.
- Theming: The output of the rendered inline tag stays always the same (and can be customized). Custom HTML markup does not allow a consistent presentation of images.
- Integration: If an image preset (image dimensions, or, ImageCache actions) is updated, all inline images will update accordingly.
- Extensibility: Once Image Assist will rely on Inline API for macro management and processing, inline tags will be customizable and extensible, and probably integrate with a lot of other Drupal modules.

HTML is always written in stone, providing none of the above benefits. Because of this, #284447: Remove HTML output feature is already a task on the list for 2.x.

I think the question has been answered. Feel free to re-open this issue, or to follow-up if you want to write a handbook page.