While both colleges are reputed, you should compare a few parameters before making a choice. Here are some of them to help you decide.

Teaching: 

Every college has good and bad faculties. 

• From what I heard through my friends at VESIT, there are few faculties that struggle with simple math problems. While some faculties from KJS struggle with simple circuits despite being electronics teachers. 
• I also know about faculties at VESIT, who are actively engaged in research projects that are respected nationally. The same goes for KJS. 

Don’t expect world-class teaching from either of these colleges. You will also need to figure out a lot of things on your own. You will also be able to figure out a lot of the study material by yourself. It will be better if you find someone, preferably a faculty to clear your doubts. 

Management: (Winning Institution - VESIT)

• As far as management is concerned, KJS recently attained autonomy so things might be a little disorganized there. At KJS you might expect odd exam schedules and late exam starts.
• VESIT does not have better management but is definitely a little more organized.

Campus Life:

• VESIT does not have a very big campus. Moreover, a number of technical and non-technical events go on at VESIT, but it is not comparable with KJS.
• In terms of crowd, KJS has a relatively chill vibe as compared to people from VESIT. But, clubs are much better at VESIT, e.g. CSI and IEEE. However, KJS also has a number of open events that you can participate in as well.

Placement:(VESIT ~ KJS)

For placements, both the institutes are almost on the same page. Here is a peek into the recent placement highlights of the institutes. 

KJS offers Mechanical Engineering, which VESIT does not. So, if you want to pursue Mechanical, KJS is a clear choice. The environment at VESIT is more suitable for technical things as compared to KJS. So, choose the institute based on what you expect out of your degree.