full range or mini's and a sub

My advice is define what you'd like and your constraints including space, budget and such.

My goal is to enjoy music and one of my compromises is no sub - and my space does allow a full range speaker.  Listen to as many different systems as you can to see what you like, don't like and potential options.

The biggest advantage with mini monitors and subs along with an active crossover, is that you can put together a world class speaker system at a fraction of the cost. The down side is that it takes a little more knowledge and skill to do it correctly.

As Erik states a satellite/subwoofer system can be magical, but done incorrectly, you can have a real mess.

Full range with subs. Or at least 3 way monitors. IMHO. 

Full size speakers WITH subs is the correct answer. There needs to be a sound power hand-off between the sub and speaker. Most subs are far more dynamic than stand mount speakers, so the speaker will still be the limiting factor. There are exceptions of course, TAD comes to mind. 
 

OP,

You ask a great question. +1 to @erik_squires.

The answer is a huge it depends. It will depend on the room and a lot about your budget and values in sound. Either can disappear. 

There are so many important aspects to the sound of a system, all of which are trade offs. Also, how much experience you have at putting together a system comes in. Integrating a sub with mini monitors can be intimidating… but if well done effective. 

First we need to know more about your room like Erik asks.

FYI, I would choose a small room over a big public space. Control is key to getting good sound. While it can be tricky getting good sound in a small room, you can get better quality equipment with a smaller space smaller speakers / amp. You can use room treatments.