Mobile search on the go is a must have for any explorers such as myself. The two notable competitors are Google and Microsoft. I have spent a good amount of time using both apps and found each of their strengths and weaknesses. Both software support the use of GPS either built-in to your phone or a external one, you just need to configure it. Also you do need a data plan for your device, it should work with any phone with Internet access. The phone I've been testing these two apps on is the HTC Touch Pro, the location of these tests is in NYC/NJ area. I will mainly be comparing the similar features and talk a bit about their unique features.
(AT&T Fuze a.k.a. HTC Touch Pro; Credit: AT&T)
Google Maps version 2.3.0.9 vs. Live Search version 3.5.8198.0
Maps
They both look great but the colors in Google Maps stands out more. Those stars on Google Maps are your saved favorites, I will get into more details about it later. If you have Location enabled, it will use cell towers to give you a estimated current position. While it's great for quick search for things nearby but it's not very accurate. Most of the time it will be off by a few blocks and I do not recommend using it if you're driving, I would use GPS. Live Search certainly have more details giving similar zoom levels, it can feel a bit cluttered. It does not offer cell tower based location and I wish it did, maybe the next update. The green flag is where you are and it's based on the last position you input.
Search

Searching is great and reliable on both platforms. Google Maps displays your last couple of search results where as Live Search only show you the last one but it saves the results somewhere else. Moving on is an example where I search for Jamba Juice.

Search results along with ratings from other customers, I like how the address is displayed. Selecting a location give you some more options.

Tap the Details tab give you more information on the business even how clean it is. Tap on See on map shows the location on map along with others. I like those big bubbles, it's easy to select with your finger.

Live Search displays way more results than Google in a compacted list. Tapping on a result shows you the address and a few other options but not as detailed. It also have ratings except they're independent from each other.

Here it displays all the Jamba Juice stores in Manhattan. The icons are smaller and needs a more precise tap from your finger.
Driving Directions
Testing the driving direction capability of Google Map. Here I want to go to Red Robin in NJ from the Jamba Juice store. It calculates it out in detail as expected.
Looking at it from the map view and on the right it's displays the traffic information. Pairing it with GPS give you precise location but a couple of things it doesn't do is keep your location on screen, go to the next turn when you hit the mark, and when I tap See as List sometimes it doesn't show the list. When you pan around, the directions disappear and you would have to tap the back button on screen. As you can see it on the right screenshot at the bottom. It's painful to drive and have to manually move on to the next turn, it can be dangerous too.
The directions from Live Search isn't as detailed but they both provided similar results.
Going into Map view with traffic enabled. The nice thing about it is the large instructions at the bottom of the screen. Tapping on the right arrow shows the next turn and vice versa. If you pair it with GPS and enable Center on GPS option, it will keep your position on screen and display the distance of your current position from the next turn. When you hit the turn it will automatically display the next turn. This is almost as good as any GPS navigation system out there except it doesn't have voice, and best of all it's free. Unlike other GPS nav systems, map updates are also free.
Other Features
Satellite view. Clearly Google Maps is a lot more clear.
Live Search can display longitude and latitude.
Google Street view outside the Time Warner building on Columbus circle.
Live Search's gas price finder and weather data.
Google Map's Favorites feature, it marks them with a star on the map. Currently there is a bug when your Favorites list gets too long it deletes them all. I'm not sure if that's intentional but it could prevent your list from getting too long. I really like this feature though.
Live Search also provide movie listing with the Movies feature, Categories if you're looking for something in a, well, category. Collections I think it's like Google Maps Favorites but I haven't figured out how to use it. The coolest feature is the voice recognition. You can search by speaking into the microphone and it's surprisingly accurate. You don't even need to train it, just tap Speak and say what you're looking for. I don't think it works well with heavy accents, nevertheless, it's awesome when you can't type.
Overall I like Google Map's cell tower location, search, and favorites list. Driving direction is not so good, perhaps it's good for walking and transit directions. Although I haven't tried those two features yet. I like Live Search's voice recognition, search, and driving direction. It would be good to be able to save some of your search results easier. They both have their pros and cons, but for quick location access I would use Google Maps and everything else either one does the job just as well.