Between Vector and Pixel graphics which one is the best to use and why?

It depends upon your requirement.
If your need is to scale the graphics to infinite then go for vector else stick to pixel.
Again for vector you need vector editing software separately.
Vector is useful and majorly use for print media.

Vector format is scalable graphics and mostly used for logos.
Adobe illustrator is quite handy, and used almost across the globe to generate the vector graphics.
Vector format works based on the points & paths.
Following are some of the vector formats: AI, EPS, PDF, SVG, and etc.
Technical term of "Pixel image" is Raster format.
It is usually used for designing websites.
Adobe Photoshop is the leading software used across the globe.
Raster format works with pixels only and it is not scalable.
Following are some of the raster formats: PSD, JPEG, PNG, TIF, GIF and etc.

Vector graphics as everyone mentioned keeps its scalability. That being said. You can use a Vector program to create anything really and make changes quickly to color, shape, layout, overall design. You cannot do that with raster. It time consuming say to redesign a web site in raster than it would be in vector. You can always convert Vector to raster as well. but you cannot convert Raster to vector.

There's no better answer but both it depends on how you play your techniques in design using that software at the same time.. :-)

 

vector is best thats what i think it also depend on job and on you also...
Vector is scalable easily editable also

I prefer to use the internationally recognized signs, and each person who can understand them is the X or the phrase "No"

Illustrator

Well both are important like you cannot convert an image to vector if you do than you loose the orignality. same with vector, but the benefit of using vector is you can stretch it as long as you want the quality will remain same but for pixel based you will loose the quality.

It depends on requirement, but in most cases vector graphics are better than raster, for scaling, crispiness and easy to edit.

The Creative design must be use Vector because vector convert any size pixel Design.It depends on requirement, but in most cases vector graphics are better than raster, for scaling, crispiness and easy to edit