I have had mixed results with my briskets, some good, some mediocre (all tasted ok if not great).
BUT, I have had a few "transcendent" briskets in my time. I usually buy sams club but honestly the best i've ever made came from my super wal-mart grocery dept. I believe that good quality meat is better, but the best brisket ive ever had was this particular one I made from Wally world.
Here's what I have learned so far.
1 - I trimmed the fat down to 1/4" cap and made sure there was no hard fat left - and I cook fat side up.
2 - Constant temp is a huge key to great brisket - if you yo-yo it's going to be a problem. Know your pit and this helps the end result. I have the best results on my electric with a digital thermostat - the temp barely moves the entire cook. (yes, my home brisket is better than my comp, sadly).
3 - Rub/seasoning/etc doesnt matter all that much, as the salt/pepper texas style is awesome without anything else. Season to your taste, but beef flavor is more important that any rub ingredient.
4 - I inject, but I don't believe in altering flavor with a bunch of crap - inject with beef broth! It keeps everything moist and you don't know it's there when it's all done.
5 - Don't know your cooker setup, but water pans do wonders for me on brisket - others will disagree, but for me this makes a load of difference. I don't get the crispy bark, it's a bit more soggy, but the tradeoff is that falling apart, fatty brisket you described. It's worth it.
6 - More cooking time helps - I hear a lot of people here asking why their brisket was tough, and they often mention they pulled it off the cooker at 180-190. Shoot for 200-205 and give it a shot.
Also - there can be a huge difference between "COMP" and falling apart restaurant style. That falling apart style would get killed by a judge, but I prefer eating it that way. A lot of advise on this forum can be aimed at comp style.
Keep it moist, keep the temp steady and let the internal temp climb a bit more. It'll be delicious.
Cat Daddy's BBQ : 22.5 WSM / Weber OTG 22.5 Cajun Bandit / Smokey Joe Gold