SUMMARY: Some thoughts on appearance and behavior.
In an online "random topic" discussion group for folks who think that Cesar Milan's training methods are abusive and represent only the ignorance of dog training from half a century ago, someone asked whether your next dog would be from a breeder or from a rescue or Other. This naturally evolved into a discussion on whether purebreds were better than mixes or rescues in various ways--temperament, bad habits or destructive instincts, physical health, and on and on.
I agree that breeding affects a dog's likely temperament or ability to do various activities, but I also agree that it's not a guarantee. Just being in agility for all these years, around huge numbers of competitors and what I'd consider to be truly responsible breeders1 and dogs who compete that are mixes, purebred (presumably) rescues, siblings from the same litter, same breeds from different litters, I've seen a huge variation in what one can expect.
One of the things that I've learned through dog sports and through two years of working to grow the [at the time] nonexistent Wikipedia set of dog articles is that people's opinions about what a breed should be, and whether cross-breeding2 is a valid thing to do, can be very strong (to put it mildly).
This is why there are different registries (in the US, anyway) for working border collies and show border collies, for working labs and for show labs, etc. I find it interesting that the AKC breed club standard for border collies describes their working instincts as the defining characteristic of the breed, yet there is no requirement for their championship that they prove it--conformation and herding are completely different tracks, so temperament and trainability and working instinct can be quite different. And that, in the world at large--by which I mean average Americans--an AKC championship, or a dog from AKC championship lines, is assumed to be the ideal Border Collie.
Or that black and brown Belgian shepherds (aka Groenendaels or Tervurens, respectively) can be born in the same litter, but by AKC rules, both parents have to be the same color and the offspring the same color as the parents or they're not "valid", whereas in other countries' breed standards, they're just types of the same breed (like different colors of cocker spaniels are the same breed) and probably have the same working instincts (depending on whether they're bred from lines with proven working instincts or from purely show lines where a heavier coat is preferred and working instinct is incidental (as with BCs).
That German Shepherd Dogs (GSDs, aka Alsatians) are very different conformationally in the US vs Europe, in that the US breed's rear legs are deemed to be more beautiful if they're very long, which means that they've been bred into having horrible hip dysplasia issues (and fear-biting is said to be more common in the American lines). That Golden Retrievers and Flat-Coat Retrievers are really the same breed--oh, no, wait, they aren't, because true Flat-Coat breeders will cull the yellow ones (is that a "responsible" breeder?), but really they'll be very similar in temperament. Here's one article talking about how these splits happen and what the possible dangers are to the breed(s) from focusing on such specific details.
My point is, if you decide that you want a specific breed, be very certain that you know exactly why you want the breed. Is it because of the way it looks? Because of the way it behaves? For example, if you want a field Lab, AKC registration isn't necessarily the best (or only) place to look; similarly with Border Collies or any other working breed. That's not to say that there aren't working dogs within AKC registries--my own BC comes from a long line of herding and (more recently) agility champions, and they're AKC registered. But they'd likely never make it in the show ring. The American Border Collie Association, however, doesn't even have conformation trials, just focuses on the breeding of working dogs.
And, of course, every breed is the result of the crossing of other breeds at some point in their history. Which, in my view, means that any crossbreed or mixed breed or whatever you want to call it--mutt--is perfectly as capable of being beautiful, hardy, healthy, intelligent, competent, and loving as any pedigreed dog, or sometimes even more so.
I find this to be endlessly fascinating; I mean it as a reminder that there's a lot going on in genetics and breeding and separation of different breeding stock that not everyone is aware of. And the results can affect your ability to get the temperament and trainability (and physical soundness) that you really want. You can't ever do that just by looking at the pedigree.
No matter their type, let your dogs know every day that they are appreciated and loved.
1Maybe another post eventually on what a responsible breeder is, in my view.
2"Cross-breeding" generally means breeding dogs of different breeds for a specific purpose. I sometimes want to extend that specific purpose to include "two dogs of opposite sex who found each other and had the specific purpose of having sex," but, eh, whatever.