I honestly find myself disagreeing with the current analysis.
Ok, now I'll give a real argument.
I assume the first thing Regidrago would do is using Dragon Energy, as it is more effective at full HP, while Regirock can either try to block or avoid, possibly with dig.
Another point is that Regidrago floats/flies, making it harder for Regirock to hit, and forcing it to use ranged moves or spend time using lock on.
In terms and status effects, Regidrago has the edge, with a wider array of attacks with those properties (dragon breath, body slam and the two fangs), against the less precise zap cannon (that would require lock on).
For stat boosts and such, they are somewhat even in terms of numbers, Regirock may have an advantage thanks to clear body, but stuff like curse also lowers its speed.
Something that turns the tables a bit is Regidrago's arsenal of supportive stuff, like screens, substitute and the useful rest + sleep talk.
Overall, I think Regidrago's takes this more times than not.
This argument relies on the assumption that both Pokemon present have access to HM/TM moves, because otherwise
Regidrago would not have access to
Body Slam,
Fire or
Thunder Fang, or the support tools such as
Rest,
Screens,
Substitute, and
Sleep Talk. We consider these outside help and, even if we didn't, I don't believe these things would actually matter:
I'll start by explaining that granting TMs you have also granted
Regirock the same
Rest,
Sleep Talk,
Substitute combination, but you have also granted it a super-effective technique in the form of
Ice Punch and another great offensive tool in
Drain Punch, this matters because
Regirock prefers physical attacks compared to the even spread
Regidrago has.
You have also put the ball in
Regirock's court this way because you've granted it
Sandstorm, which will not only harm the Dragon-type over time because it lacks the favorable typing, but it will boost the Rock-type's Special Defenses by %50; a Pokemon like
Regidrago relies on both its precious health and Special Offence because it has no way to boost
Dragon Energy, which will be getting weakened throughout the battle because the only boost it has is in
Dragon Dance which will only boost physical moves.
But now allow me to get into the main part of my argument, which will rely on level up moves only:
Regirock is a defensive Pokemon with a base 200 in Defense but 100 in Special Defense, why does this matter?
Regidrago's moves are primarily offensive, including its super-effective move in
Hammer Arm, this is why it comes prepared with
Dragon Dance. This means that its primary method of attack is countered by the much superior defenses and its most powerful move
Dragon Energy isn't supported by the majority of its kit.
Contrary to this,
Regidrago is a glass cannon, its defenses are much smaller by comparison to its offense, both sitting at a base of 50. This means the
Regirock is going to be considerably more effective with its offense (Both of them have an Attack stat of 100) which is the majority of its kit as well.
It begins to fall apart for
Regidrago because it lacks a method of actually boosting its defenses, while it has
Dragon Dance to boost Speed and Attack,
Regirock comes prepared with
Curse to increase its own Attack while also increasing Defense, just at the cost of Speed. Alternatively it also has
Iron Defense, which will still keep it ahead of
Regidrago's boosts because it increases defenses twice per use instead of once like
Dragon Dance.
You could say both have
Ancient Power to provide stat boosts across the board, but that is
Regirock's typing, meaning it is still more effective with the move regardless. The same could also be said for
Explosion, because not only is
Regirock naturally more equipped to survive an
Explosion from the Dragon-type, it also resists it by virtue of being a Rock-type, meaning that even that will be much, much more devastating in the use of
Regirock.
If we assume both parties are fighting each other optimally, you could assume
Regidrago goes for either
Hammer Arm or
Dragon Energy to start which will hurt, sure, but
Regirock comes equipped with
Zap Cannon for a guaranteed paralysis. which will be much more crippling as it will result in only one Regi fighting at full capacity whereas the other will have a hard time moving.
I believe
Regirock wins this
7/10.