Three Questions, for now...
 

What hotel is better? Or what is the difference between the two?Sheraton Manhatten or the Sheraton NY...

What area are these hotels in?

Would you take the subway or a cab from the Airport, either LGA or JFK. We are familiar with subways, just not NY.

You need to repost with a title like Hotels and Transportation in NYC

Fodors is confusing about how they handle messages. You think you are posting in a NY forum, but you are posting in a USA forum and really only tagging NY

Seems like both of these hotels are just north of Ties Square, just a few blocks from one another.

<<Would you take the subway or a cab from the Airport, either LGA or JFK.>>

There is no one answer to this, since different modes of transportation work better for the different airports.

Subway does not go to LGA. There is a city bus to subway connection that some might or might not recommend. However, if there are at least two of you, most would say to take a taxi (costs $30-$40 including tolls and tip).

For JFK, Airtrain to subway or LIRR is a reasonable choice to many. Taxi costs more than from LGA ($55-$65 including toll and tip).

north of TiMes Square

I have have stayed at both in the past. The 2 Sheratons are on opposite corners from each other on 7th Ave, which is MID TOWN. A very central area for getting around Manhattan. Times Square and Central Park are walkable :) Both have small rooms. The main difference is the Towers is bigger and much busier IMO.

I have only come into JFK. I have taken the New York Airport Service Express Bus that goes to Grand Central and smaller vehicle then to the hotel from there as well as Super Shuttle. I liked super shuttle for not having to deal too much with my luggage ... but it takes a while to do all the pick-ups. The bus is easy to catch from all the terminals and they run on a schedule.

Both of those Sheratons are tired and in desperate need of renovation. I don't recommend either. Read the reviews on tripadvisor.com if you haven't already. They are 2 blocks from each other in midtown west. If you have to use a Sheraton hotel, the Four Points Chelsea is very good.

From LGA, a taxi is always best for 2 or more people. From JFK, it depends on where you're staying, your budget and how much luggage you have. Taxi is fixed rate of $45 plus toll and tip or ~ $60 total. There are express buses that go to Port Authority or Grand Central for ~ $15/person (do not use shared vans that drop people at individual hotels).

The hotels are diagonally across the street from each other on Seventh Avenue--the Sheraton NY on the east side of the street between 52nd & 53rd Streets; the Sheraton Manhattan is on the east side of the street between 51st & 52nd Street. Thus, they are few short blocks just north of Times Square.
The Sheraton NY is a little better than the Sheraton Manhattan, but the latter one has a swimming pool.
They're basically hotels for business people. I don't think they're as bad as some of the previous posters have said. If you can get either from Priceline or another discount source, I say, take the room.

I stayed at the Sheraton New York recently. It was totally acceptable. No complaints from me. Not an elegant, luxury hotel, but location is great, room was okay, service was fine.

Correction on my previous post. It should have read that the Sheraton Manhattan is on the WEST side of Seventh Avenue.