I have 6 horses right now.  Four are kept at home and two are at a trainer/instructors.  There are aspects of each that I love and aspects of each that I don't.

At home:  I am much more connected with the horses at home.  They are the horses that can be taken riding anywhere and anytime.   I love them galloping up to be fed and seeing their faces every day.  The daily "must do" routine is feed/H2O (no stalls) and takes less than 20 min. total.  Of course, they are ridden and so more time is spent with them then just the 20 min care.  Travel takes some planning but is not impossible.  This connection, however, does not extend to competition as the home set up (trail riding only on hard packed and uneven surfaces with "mystery holes") and irregular riding schedule is not ideal for some types of schooling  

At instructor/trainer:  These horses are much more polished.  There is a nice arena with great footing set up with challenging obstacles.  Also, having an instructor and other riders to be with means we are pushed to perform at a higher level.  However, there is less personal connection with these horses and it is a pain to drive out there.  

The worst part is that because the trainer rides them regularly, we just "catch up" to what the trainer is doing with them rather than having real ownership of their training.  But, this is the really best way to progress in ones riding abilities.  I find that I ride my "at home" horses much better now also.

Ultimately, though, I can see a time when I don't have horses at the instructor/trainer any more but I wont give up the horses at home.