Excellent essay on the subject by Krishna Subramarian on TechCrunch:
Clash of the Titans: The Battle To Become The Mobile Search Leader.

The essence is well summarized in the introduction:

Mobile search is still one of the big unclaimed prizes on the mobile web. Everyone from Google and Yahoo to Apple is going after it, but Microsoft’s Bing may stealthily become the king of the castle by aggressively promoting Bing through mobile apps. Let’s look at each player’s mobile search strategy.

Update: there is a specific battle under formation in China which could significantly alter the worldwide search SaaS battlefield as well
– China Mobile Challenges Baidu With Plans for Online Search [Sept 16] which is making the mobile operators’ position pretty clear by observing that: « The operator joins carriers in the U.S., Europe and Japan in turning to data services to spur earnings as the Chinese phone market saturates. “For China Mobile to get a meaningful contribution from new businesses, they really have to turn into big successes to make a difference, as the company is so big,” said Jim Tang, who rates the stock “neutral” at Shenyin Wanguo Securities in Shanghai. “China Mobile gets about 70 percent of its revenue from voice, and growth is completely flat there.” »
– China Mobile: 4G network coming soon [Sept 15] is stating that “4G data card is close to debut and the carrier and partners are working on the research of 4G handset chip … China Mobile is expected to launch 4G mobile communication services as early as 2011 to boost its high-margin data services, according to the GSM Association.”
– China Mobile to set up device sourcing company [Sept 17] is telling that “The planned device-sourcing company will begin to purchase TD-SCDMA-enabled [3G] feature phones with prices below 1,000 yuan (US$148) at the end of the year and then shift to smartphones [likely with integrated 2G, 3G and 4G] priced below 2,000 yuan in the first half of 2011″.

Background information on this blog:
– 3.9G TD-LTE rollout in 2012 with integrated 2G, 3G and 4G? [July 19, with updates till Sept 17 and beyond]
– OPhone OS (OMS) 2.0 based on Android 2.1 [July 5, with updates till Sept 17 and beyond]