How to deal with guilt turning down non-tenure track faculty offer at current institution?
If they really wanted you (or anyone) enough, they would make the position more desirable (tenure, pay, etc.).  They do it for other positions.

Don't you worry yourself a bit.  Be pleasant on the outside, sure.  But realize this is a business situation.  You have competing offers.  Take the one that does more in terms of pay/etc.  

Also, often to advance in life, you need to move around some.  That's nice that you have a cozy situation there and people that value you.  But move on and do it elsewhere.  It's not unusual for companies or organizations to pay more for someone external than someone internal.  

In particular, it is completely normal for someone in your situation to move on (recent grad).  If anything hanging out at your school is more the oddity.  So nobody will care that you moved on. Will wish you the best.