I am new here but According to me remote blog is better like on blogspot etc as you can customize domain and script on it, it saves bandwidth, if your server becomes down it will remain up, from point of seo also it is better
Having a blog with a third party provider has some drawbacks. One problem is incoming links which do not point to your domain. If you decide to move to another blogging provider on some point, you will loose all incoming links and all incoming traffic from search engines may become useless.
Another problem is integration. If your current site has a user list, you could integrate that list with your own blog for example. Other features like menus etc can also be more easily integrated if the blog is hosted on the same domain as the rest of the site.
I would like to look at this differently. If your idea is to draw traffic to your site through blogging then you may want to look at setting up blogs on major 2.0's such as a wordpress, blogger or Squidoo. Remember they carry a lot of authority on Google and hence they are more likely to rank faster than your private domain blog. Once you have started to pick up some decent PR, you might want to look at having more content on your site through the form of blogging. This helps increase the CRAWL BUDGET for your site too which in turn improves crawl rate and hence the ranking should follow soon.
But I am pretty sure this is not the only way to do it. This is one of the strategies that we've tried implementing in a large scale for acceptable effectiveness.
I hope this helps if not DO NOT hesitate to ask questions.