The most simple answer is what you've already found: draw everything internally to a RenderTarget with a fixed resolution and after that use the RenderTarget as a texture and draw it as large as possible. You should be able to fill the entire screen if the aspect ratio is the same. Simply use the Spritebatch.Draw overload that uses a destination rectangle. If you use an internal resolution with an aspect ratio of 16:9 then you should create a rectangle like this:
//If the internal resolution and target resolution are both 16:9
Rectangle dest = new Rectangle
(
0,
0,
graphics.ViewPort.Width,
graphics.ViewPort.Height
);
//If the internal resolution is 16:9 and target resolution is 4:3
int height = (int)(graphics.ViewPort.Width * (16.0/9.0));
Rectangle dest = new Rectangle
(
0,
graphics.ViewPort.Height - (int)(height / 2.0),
graphics.ViewPort.Width,
height
);
Another approach would be to make sure that all text and GUI elements are withing a safe in the render target that has a 4:3 aspect ratio and then simply discard the most left and right part on a 4:3 screen. (This might give players with a 16:9 aspect ratio an advantage since they will have a larger FOV).
Tip: if you are developing your game for the XBOX360 you can jus develop for one resoltion since the XBOX will do the up and down scaling automatically for you. You should use an internal resolution of 720P since this is the highest resolution that the XBOX upscaler/downscaler can scale down to old-TV resolution.
Edit:
See the comments: the general formula for the destination rectangle that works for all aspect ratios where width >= height would be:
double aspectratio = ((double)graphics.ViewPort.Width / (double)graphics.Viewport.Height);
int height = (int)(graphics.ViewPort.Width * aspectratio;
Rectangle dest = new Rectangle
(
0,
graphics.ViewPort.Height - (int)(height / 2.0),
graphics.ViewPort.Width,
height
);