The problem is that the clip boundary is not being anti alised.
To solve you can render the shape without using the clip. The ctx.arc method lets you set the start and end angles so you can get the inset by filling two arcs.
You will need to get the angles where the clip circle and the inset circle intercept.
For this case it is very simple. First get the distance between the circles, and the angle from one to the other. This works only for two circles of same radius.
var c = {x:?,y:?}; // circle one location
var c1 = {x:?,y:?}; // circle two location
var radius = ?; // radius of both
var angle = Math.atan2(c1.y - c.y, c1.x - c.x); // get the angle from one to the next
var dist = Math.hypot(c1.x - c.x, c1.y - c.y); // get the distance. NOTE IE does not have hypot so do it the normal way with Math.sqrt....
Now you have the angle and distance the intercepts are a simple relationship between the distance and the radius
var iAngle = Math.acos(dist / 2 / radius); // the angle from the line between the circles
// to the intercepts
Now you have that angle you can draw the two arcs
ctx.beginPath();
ctx.arc(c.x,c.y,radius,angle - iAngle , angle + iAngle); // first arc
ctx.arc(c1.x,c1.y, radius, angle + Math.PI - iAngle, angle + Math.PI + iAngle); // second arc
ctx.fill();
ctx.stroke();
There is not much you can do to prevent the jaggies from effecting the clip area. Another way to achieve clipping is to use ctx.globalCompositeOperation to render a mask. You can mask in and out, and many more options. This will be a better solution when the clipping area becomes more complex.