Spring mattresses are usually made of three distinctive parts: the foundation, spring-core and upholstery layer(s).

The main difference between Box springs mattress and an ordinal mattres is its Foundation part. This foundation is made of extra-heavy-duty springs. This type of foundation has softer support than mattresses with traditional wood/steel foundations.

Pros of box-spring mattress:
Mattress with box springs foundation is much softer/bouncier than the ordinal one.

Cons:
Higher price comparing to mattresses with traditional foundations
A bit weighter because of massive steel springs, a bit harder to move / clean

How to choose a good box-springs:
Test it before buying to feel the difference. If you don't like the softness - try another one.
Choose one with high-density block of foam under the box-springs ( or search for a rigid foundation ). This is because massive springs can sag into bad foundation.

Conclusion:
I think it is worth to get mattress with box-spring foundation. Yes it is bit expensive, but it is a good choice if you seeking for extra-comfort.