What are the main difference in obligations of both MIT and X11 license. How do they differentiate or there is no difference and can be used in replacements.
The MIT license comes in two variants which we'll call Expat and X11. The X11 variant includes an extra paragraph like this:
Except as contained in this notice, the name(s) of the above copyright holders shall not be used in advertising or otherwise to promote the sale, use or other dealings in this Software without prior written authorization.
Furthermore, there are countless MIT variants that substitute “the authors” or “the copyright holders” with the name of a particular person or organization.
The anti-advertising clause from the X11 variant can be interpreted to impose an extra condition on the license. Then MIT/Expat → MIT/X11 is compatible, but MIT/X11 → MIT/Expat is not compatible. Here, the compatibility relationship “A → B” would mean “software licensed under A can be distributed under terms B”.
Alternatively, that paragraph can be interpreted as a basic reminder of what is and isn't allowed, without changing the rights of the recipient: you're not allowed to advertise with someone else's name whether or not you use their software. Under this interpretation the two license variants are effectively interchangeable.
Even when the variants are compatible or interchangeable, the license requires the complete license to be kept intact – once you receive the license, you cannot replace it by another MIT variant.
But for your own software, the choice between the variants is effectively arbitrary. In practice, the Expat variant that doesn't have the extra paragraph is used more widely. This variant is what most people think of when they hear “MIT license”.