In certain cases, portfolio-only sites work well. And depending on the types of clients you have, a blog would be somewhat useless for you.
But if your site is the main way people reach you, then you would most probably greatly benefit from having a blog. It’s a great way to show your personality, to create a more personal connection with your audience. And you get the freedom to list all your gear, showcase your recent projects, share tips & tricks.

From an SEO standpoint, a blog offers a lot more content for search engines to “digest”, it can help you rank higher in search results for certain keywords.
With this in mind, keep the blog under the same domain for the most SEO impact, otherwise you’re confusing both people & search engines, you’re splitting your work in two for no valid reason.
So don’t forget that people also love blogs, they are dynamic, they are fresh (if you keep them fresh), they’re a great way for them to stay up to date with your work.

At a minimum, you can get away with just spending 15-20 minutes a day adding content to your blog, so it doesn’t really take up that much of your time, something photographers are sometimes afraid of.
Ideally, you shouldn’t use the blog as a simple portfolio (just publishing your images), but instead write actual text too: your projects, experience, equipment, stories etc. But try not to mix work-related posts with personal/family photos, your audience might start losing interest.
But only invest time in blogging if you’re doing it for the right reasons
A blog can be a power marketing tool, but not if you’re using it to post family photos or cover mundane topics. The days of the traditional blog posts are over, you now have to be more creative and focus more on storytelling.
You can not establish a name for yourself as a photographer (or get ahead in the business) if you just keep an “online journal”.
Your blog should instead serve your main website’s purposes, whatever they might be: promoting your work, helping you sell images, getting you in touch with more/better clients etc.

And by all means, don’t blog only for SEO. Even if you’re working hard to optimize your posts for Google’s eyes, make sure you’re also writing quality content for humans (great storytelling, personal recommendations, honest opinions). Stuffing your blog posts with keywords can make them “smell” of spamming, you risk alienating your audience.
Lastly, don’t over-sell things. It’s natural to try to also promote your services/products on your blog, but doing it too often looks really bad, so try limiting it to 10-20% of your content updates. (Same applies to any social media updates.)
Further reading
For inspiration, check out PhotoShelter’s Blog Handbook (contains many examples & tips from successful photo bloggers):

Other relevant articles about blogging: