Perks of showing?

So I've been bouncing between showing and the riding school to train my babies.... I'm starting to really like the riding school since it seems to give them a lot more stats then showing. What are y'alls thoughts? People seem far more interested in stats then in points I've noticed.... Are there perks to showing that I'm not aware of?

Showing has the potential to give you more stats, and good show horses are things people look for (what with non-specialty stats etc) 
I use both interchangeably, so take my opinion with a grain of salt, lol.

Riding school can give you items, I don't believe showing does. Showing gives you player points, riding school doesn't.

Riding school can give you a max of 10 stats in a day, the max stats from showing in a day is 30. 

A good horse at the top of it's showing grade can easily get 10-15 stats in a day (there are foundation horses that can do this too, but you need to be very picky when you get them from the EC). 

Riding school averages out to 3 stats a day (I actually did the math once) + haycubes can bring your daily average to 5 stats a day (again I actually did math for this) + peppermints would be even more (no math done for this one 'cause peppermints are too expensive for my tastes)

If you show or do riding school you get 11+ stats every ten days from training your horse. 

I feel that riding school is great for horses that aren't born to show (have higher than 65 non-spec stats), but you get more stats in the lifetime of a horse with showing (if you show consistently, and do it by hand as opposed to auto-shpwing). Also I like to use the riding school for horses with 20-65 non-spec stats except when the horse is at the top of its grade.

You don't always have to do one or the other!
I use both. When the horse is at the bottom of its grade I enter into riding school, and when it is at the top (20 away), I show.
For example 100-129 I enter into riding school. 130-149 I show. Then 150-179 riding school, 180-199 showing. 

I'm slowly working into doing more showing, I just don't have the personal time right now to hand pick shows for every one of my horses (or at least the show quality ones with good non-spec stats). I prefer not to do auto showing. 

I do it exactly like Saber, although I haven't been showing many of my horses recently, cause they don't have any tack and I was too lazy to buy some and then upgrade it. lol. xD
But some of my horses aren't really born for showing, they hardly ever place. So those go into the riding school everyday, regardless of their current stats. 

I also do the same as Saber. I just started with a giant herd of foundations, but I've been keeping an eye on how much money I make, how many stats I get, and just actually added an average stat column to my spreadsheet. 

I'm only on day 4 of this method, but you're welcome to take a look at my numbers so far: Google Spreadsheet