Both options look fine. I assume you are returning the parentPage object reference in option 1. Do you get an error message? What exactly do you mean when you say both options don't work?

Below is an example of both options which work fine. 

<apex:page controller="mySecondController" tabStyle="Account">
    <apex:sectionHeader title="New Account Edit Page" />
    <apex:form>
        <apex:pageBlock title="Create a New Account">
            <apex:pageBlockButtons location="bottom">
                <apex:commandButton action="{!save}" value="Save"/>
            </apex:pageBlockButtons>
            <apex:pageBlockSection title="Account Information">
                <apex:inputField id="accountName" value="{!account.name}"/>
                <apex:inputField id="accountSite" value="{!account.site}"/>
            </apex:pageBlockSection>
       </apex:pageBlock>
    </apex:form>
</apex:page>

public class mySecondController {
    Account account;

    public Account getAccount() {
        if(account == null) account = new Account();
        return account;
    }

    public PageReference save() {
        // Add the account to the database. 
        insert account;

        // option 1
        return new PageReference('/' + account.Id);
        // option 2 
        //return new ApexPages.StandardController(account).view();
       
    }
}

https://developer.salesforce.com/docs/atlas.en-us.apexcode.meta/apexcode/apex_system_pagereference.htm