wait.until(ExpectedConditions.visibilityOf Element1 OR Element2)

Now there's a native solution for that, the or method, check the doc.

You use it like so:

driverWait.until(ExpectedConditions.or(
    ExpectedConditions.presenceOfElementLocated(By.cssSelector("div.something")),
    ExpectedConditions.presenceOfElementLocated(By.cssSelector("div.anything"))));

This is the method I declared in my Helper class, it works like a charm. Just create your own ExpectedCondition and make it return any of elements found by locators:

public static ExpectedCondition<WebElement> oneOfElementsLocatedVisible(By... args)
{
    final List<By> byes = Arrays.asList(args);
    return new ExpectedCondition<WebElement>()
    {
        @Override
        public Boolean apply(WebDriver driver)
        {
            for (By by : byes)
            {
                WebElement el;
                try {el = driver.findElement(by);} catch (Exception r) {continue;}
                if (el.isDisplayed()) return el;
            }
            return false;
        }
    };
}

And then you can use it this way:

Wait wait = new WebDriverWait(driver, Timeouts.WAIT_FOR_PAGE_TO_LOAD_TIMEOUT);
WebElement webElement = (WebElement) wait.until(
        Helper.oneOfElementsLocatedVisible(
                By.xpath(SERVICE_TITLE_LOCATOR), 
                By.xpath(ATTENTION_REQUEST_ALREADY_PRESENTS_WINDOW_LOCATOR)
        )
);

Here SERVICE_TITLE_LOCATOR and ATTENTION_REQUEST_ALREADY_PRESENTS_WINDOW_LOCATOR are two static locators for page.

I think that your problem has a simple solution if you put "OR" into xpath.

WebDriverWait wait = new WebDriverWait(driver, 60); 
wait.until(ExpectedConditions.visibilityOfElementLocated(By.xpath("//h2[@class='....'] | //h3[@class='... ']"))); 

Then, to print the result use for example:

if(driver.findElements(By.xpath("//h2[@class='....']")).size()>0){
       driver.findElement(By.xpath("//h2[@class='....']")).getText();
}else{
       driver.findElement(By.xpath("//h3[@class='....']")).getText();
}