On a mac you don't need to delete advanced machines or nether ores. I use a mac all the time and to run a tekkit server you will need to install Java 7 as funny enough the tekkit launcher only works with Java 6 and the tekkit server only works with Java 7. To check your installed java versions, open the java-preferences program (spotlight it) and see if you have the required java versions and if they are turned on. If you don't have java 7, download and install it from http://www.oracle.com/technetwork/java/javase/downloads/jre7u7-downloads-1836441.html . If you already have it, make sure it is turned on and standing at the top of the list as that will then be the preferred java version when a java program launches. From that moment on you should have no trouble starting and using the server. If you want to play on the same computer as you run the server on, you should (while your tekkit server is already on) switch back to java 6 in your java-preferences and then start the tekkit launcher. Skipping this step will constantly crash your launcher .
The method is a bit unhandy bit as far as I know it is the only way to have both programs running on mac. I use version 10.8.2 . Tell me if it worked for you
P.S. If you delete only these 2 mods you will miss this and this