To be honest with you, if you read the Richard Dragon mini-series (a VERY good mini-series, and if it was a stock I would recommend it as a definite buy) you will realize that Dragon is better.
Both of them are in it, and Dragon starts off as a student in a dojo owned and managed by Tiger. He is raised up to be hard and tough, and goes to win tournaments and what not (where he first meets a young Lady Shiva, the first of many meetings between the two). To cut a long story short, and without spoilers, there is a falling out between Dragon and Tiger, and Tiger catches up with him years later where Dragon is fighting skilled fighters in a pit tournament ....with those fighters having knives ....and Dragon being blindfolded.
Some words are exchanged, and it is inferred that Dragon could take Tiger, and do so without much difficulty.
Anyways, the series continues, showing how Dragon trained many people (including a certain man called Bruce Wayne, as well as several of his proteges), encounters with the League of Assassins, meet ups with Connor Hawke, and obviously how he was close with Shiva (including how both can use the leopard strike ....when you drive your fingers through someone's skull into their brain).
The finale is a fight for the no.1 martial artist title, with all sorts of DC martial arts luminaries (ranging from the monkey cult to all sorts of folk), until at last it is between Shiva and Dragon.
I will not say who wins, but it was a great fight.
Anyways ...back to topic ...Richard Dragon would defeat his former teacher.
(And just in case you are wondering, in a hand to hand fight he would beat up Batman as well).
The top-3 in DC are Richard Dragon, Lady Shiva, and Cassandra (Batgirl) .....they alternate in who is no. 1, but those are the top (you can consider all of them as being number 1 at the same time, with one or two being better than the other depending on depiction).
Obviously there are people who are better (e.g. Karate Kid, who is the best ....but his level is so high that including him is unfair), and there are others who are good enough to be a challenge to the Top 3 (e.g. people like Mad Dog) .....but the top 'nomal' three are Richard Dragon, Lady Shiva and Cassandra (in any order ....consider all of them to be simultaneously in the top 3).
Bronze Tiger is not in the top 3, but he is easily in the top 10. He is also crazy good.
However, by the time they were splitting ways, Richard Dragon was already better than Tiger. By the end of the series, Tiger was not even in the tournament of martial artists, and in that tournament only one person faced off against Shiva.
The way I look at him is that he is the Shang Chi of DC (and no, do not ask who can win .....in my opinion they are perfectly equal, with equal skill levels and equal feat levels. The only way person A would say Shang Chi wins, or person B say Richard Dragon wins, is if person A is a fanboy of Marvel and person B a fanboy of DC. They are equal).
If you did the same you would not have asked that question (although I guess it is to be expected, since just yesterday you were saying that the Punisher, with a sword and dagger, can defeat Wildcat in hand to hand combat).
You saying that Bruce is 'clearly superior or stalemates Shiva' just proves what I said on the other thread ....the results of relying on wikipedia entries (or for the slightly more advanced noob looking at stand-alone scans) are quite evident.