domain.mobi (Subdirectory)

Pros

• Carrier transcoding. Sprint PCS in the US and Vodaphone in the UK transcode (modify websites) that you load on your phone for the best experiences (although, it breaks some websites). These carriers assume .mobi is mobile-friendly and do not modify their content.
• .mobi means mobile-friendly and is best for search: Some search engines can be set to only search .mobi domains with the assumption that they're all mobile-friendly. Although, this area is very new and search engines can determine a mobile-friendly site via other methods, this is one area of speculation.
• Brandable. Some might say that .mobi is more brand-able than m.domain.com. For instance, it's easier to tell people to go to http://domain.mobi and build a campaign around it than http://m.domain.com.
• Separate control. This might be important for an agency who is building a mobile website for a client. If they wanted to purchase and host the domain names themselves, they can. This can speed up the process for getting a domain established for the mobile site.

Cons

• Opportunity for domain squatters. Several companies own their domain.com, but they don't always own the .net/.org variations. This could either be due to never having thought about it, lack of interest, or the .net/.org being owned by a domain squatter. The domain squatter also has the opportunity to purchase domain.mobi
• More effort to type. .mobi takes longer to type than .com thanks to the .com button on most smartphones. At the end of the day, a .mobi domain isn't needed much.
• New domain, no SEO juice. A .mobi domain would be treated as a new domain name and it wouldn't take any SEO from whatever current domain you have.
• Costs involved and inconvenience. The cost of a .mobi domain and added inconvenience for managing it may not make it worthwhile.

m.domain.com(Subdomain)

Pros

• Easier to access and maintain. The DNS is all stored under the same domain. No additional domain to purchase, set up, and manage.
• Easier to type on a phone. iPhone and Android on-screen keyboards include a .com button on the virtual keyboard.
• Keeps your brand in-tact. People already know domain.com is yours. Something like domain.mobimight confuse them.
• Free. Setting up a subdomain should be a simple process depending on the web host.
• Higher adoption in the US. Companies such as Yahoo, Twitter, Google, YouTube, and Facebook have adopted this method.
• Support for multinational domains. Some companies such as Amazon have Amazon.com for their US presence and Amazon.co.uk for their UK presence. A .mobi site just comes in .mobi. I suppose you could have co.uk.amazon.mobi, but that sounds messy (and backwards). m.amazon.co.uk makes more sense.
• It's what Matt Cutts said. Matt, who works at Google and shares webmaster tips for best practices, suggested that m.domain.com will do the trick.
• _Cookie support. _This may be one of the greatest benefits of the m.domain.com method. Cookies, or temporary files on your computer used to store information, can be set for a domain and a certain subdomain. With domain.mobi, however, cookies cannot work across multiple domains. So, if you logged into a mobile website but needed to view the desktop website and wanted to switch to that mode, using m.domain.com would be best so you can stay logged in between both sites.

Cons

• Too ambiguous. Some would argue "m.domain.com" makes no sense and isn't intuitive for people looking for the mobile site.
• No carrier transcoding. Few phone carriers are transcoding websites so when someone access a site on their phone the website gets reduced in size so it loads faster. This could break some desktop websites and mobile sites. Only Sprint PCS in the US and Vodaphone in the UK are doing this that we've heard of. The work around is to manually register your mobile website as a mobile website with each carrier.

One question I often hear is which makes more sense for someone to type in, m.domain.com, or domain.mobi? My answer: if you want the mobile version, go to the desktop site and it should take you to the mobile version.

If in doubt, use m.domain.com and redirect the domain.mobi to m.domain.com.

This was the more common method of delivering a mobile optimized website before responsive design came along. You have a mobile site on a different sub-domain, such as m.bbc.co.uk, keeping all of your mobile content on different URLs.

The two most important points if you’re using this method are:

Use the rel=”alternate” tag pointing to the mobile URL on the desktop version of the page, helping Google find your mobile content.

Use the rel=”canonical” tag pointing to the desktop URL on the mobile version of the page, helping Google understand which version of the content is duplicated.

**At the last my suggestion is go with subdomain for mobile website. **

Let me know if you need more help.

Hi,

I am agree with @Takeshi Young.

It will not give you any direct benefit. Although It may be helpful in improvement of you Click Through Rate(CTR) that will give you indirect benefit for your SEO campaign.

Home page backlinks will distribute the link juice on whole inner page. Most of the time home page gets backlinks because of the most prompt page of the website. But it also depends on  the most relevant link concept. If your inner page is best relevant  for getting any backlink then you should choose inner one.

But most of the backlink provider resources(directory, forum signature etc.) prefer home page of websites.