What framework is more friendly and open towards css customisation? How ugly will it get? Ideally they should look and behave exactly like their kendo counterparts.
(To give some context: I have to choose between the two frameworks and maybe later will hire a webdesigner to mimick Kendo's web UI look & feel.)
As an example: Kendo's calendar picker UI http://demos.kendoui.com/web/calendar/index.html
That date picker seems pretty standard fair. Dojo's picker (the one I am most familiar with) will handle it.
The skinning will be the trickier part. Dojo has good theme support, so you should be in good shape there, but it will still require a lot of effort to get things looking the way you want. (Having a web designer will be a big help).
What I would do if I were you is look at your project, and see what widgets are must have, then make sure whatever toolkit you go with has them.
I would be surprised if any prime-time JS framework didn't include skinning support that would handle the look and feel you want to add. Still, you are going to have to dig into that support and learn it, and end up dealing with a lot of pretty involved layout and CSS.