I've noticed that on most shows, the secondary sets (usually a neighbor or relative) aren't as nice as the primary sets. This makes sense as the budget would go into the star's set.

The Jeffersons--George and Weezy had that deluxe apartment in the sky. On occasion, we would see the Willis's apartment, and it was a scaled down version, not nearly as lavish or spacious--and in the same building no less.

Rhoda--Rhoda had the nice apartment, while her sister Brenda lived in a two by four.

The Bob Newhart Show--Bob and Emily had the sprawling, beautifully decorated apartment, while their neighbor Howard had a small, simply furnished place across the hall.

I'd guess that 90% of the home set design budget on The Sopranos goes into the Soprano home.

There are exceptions. On Mister Ed--Wilbur and Carol Post's friends, the Addisons, live next door. The Addison's home is every bit as spacious and elaborately decorated as the Posts.

Any examples or exceptions to the rule?

I guess a secondary set on Cheers would be ...the office? And it was still pretty decorated.

and if that doesn't count because it's still withing the bar then

Dianes apartment, Melvilles, Gary's old time tavern, Rebecca's apartment, Frasier and lilith's house, Carla's house...they were all decorated to their style.

Secondary sets, or "swing" sets, aren't used in every episode, so usually have to be assembled and broken down when needed, so they aren't as elaborate as the main sets.
Also, stage space is pretty tight in a TV studio, so those sets for the most part are smaller.

Beginning scriptwriters are often encouraged to write spec scripts using only main characters and main sets, to keep costs down and make filming less time consuming.