I've done both with my Boxers.
My old veteran (RIP) had her Good Citizens Bronze, Silver and Gold.
She showed and had won many Best Veteran classes.
She was obedience trained as a pup, although not to competition level.
My Boxer bith 4yo. Has got Bronze and Silver awards, not obedience
trained as such, neglected as concentrated on showing. Paying the penalty now. A REAL HANDFUL. She's got the brains to do it so we are re-training at the obedience side slowly.
My pup now nearly 11 months old, does both obedience training and
ringcraft. Yes the only problem was the stand & sit training as I do use
bait for showring and titbits for training. But she's fine now, just a few training tweaks. She almost passed Bronze GC test but failed on the
sit/down stay of 1 minute (she stayed for 40 secs). Her confidence has taken a bashing after artillery fire at a local MayFayre. So any loud noises she wants to be with me. Still with time I'm sure she'll make it

The only thing I do is use a different lead & collar for the training at
obedience. (normal webbing collar and lead) Show ring she has a choke chain and different colour lead. The two that I did do both, enjoy using the brains and it's a valuable socialising place at a good training class.
Hope you have lots of fun.
Kind Regards
Kirstine