It depends on your CMS. (wordpress post are indexed quickly). If both of them have the same CMS, you have to earn some link juice on the new blog.

it usually take sometimes for the the domain to be trusted by search engines.
You can try to add in more ping sites on to your CMS if you are using wordpress it is at Setting --> Writing --> update services

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If you want to increase your crawling rate then you need to add content on regular basis otherwise you can increase your crawling rate by doing social bookmarking as it is consider as one of the best method to index your site or blog fast.

one week ago Google published news about crawling and indexing in that new Google told that Google slow the crawl for some reason.If you need more information about then click on it Google Crawl

There are two methods you can use to get your posts indexed fast.

1) Ping your posts after you have written them, by pinging the pages that your posts are on you tell the crawlers that these pages have been updated and invite the robots to crawl your pinged pages. You can check out pingler.com

2) The second method is to use social bookmarking, the bots crawl the social bookmarking sites very often, and if your posts are bookmarked then the crawlers will follow the link from the bookmarking site to your new posts.

Hope the info helps.

Crawling means sucking content without processing the results. Crawlers are rather dumb processes that fetch content supplied by Web servers answering requests of requested URIs, delivering those contents to other processes, e.g. crawling caches or directly to indexers.

Indexing means making sense out of the retrieved contents, storing the processing results in a document index. Link analysis is a way to measure URI importance, popularity, trustworthiness and so on. Link analysis is often just a helper within the indexing process, sometimes the end in itself, but traditionally a task of the indexer, not the crawler (high sophisticated crawling engines do use link data to steer their crawlers, but that has nothing to do with link analysis in document indexes).