I'm moving to another home. Should I keep my house and rent it or sell it?
This is a question that generates more questions. Do you need the equity from the first house to purchase the next one? If you were to refinance the first home to generate equity to buy the second home, is that plausible?
I'm going to frame my answer around the premise that you can keep the existing house with reasonable leverage. If that's the case, then the first thing to do before moving is to refinance the 1st house to an appropriate level and make that equity available for another investment.
Concurrent with completing this refinance, it's essential to look at loan-to-value secondarily. The American way is always to maximize refinance proceeds. What's more important is to make sure the leverage used is such that rental income will cover the mortgage payment plus taxes and insurance and reserves (reserves for replacements of significant system failures or functional obsolescence).
It's always better to refinance a property as an owner/occupant versus an investment property; interest rates are better for owner/occupants, and sometimes fees are also less.
It's worth refinancing if you are planning on a long-term hold time, and you can reduce your rate by 1/2% or more assuming fees are reasonable. The best of all worlds is that your new mortgage is a payment less than the original mortgage, and there is some cash out you're finished. That's a win-win on two fronts; a lower payment plus cash in the bank.
Taking a different view, if purchasing the new home requires maximum leverage of the existing house, it's probably better to sell home #1 to buy home #2. Why is that? The primary reason is because of the excess leverage created from attempting to keep home #1.
Max-leverage will sometimes create negative cash flow on the rental house concurrent with the added stress of everything having to go perfectly (every month) to make both payments on both homes. This assumption requires that all rents are collected all the time, and there's never a missed rent payment from your tenant. And we all know that life doesn't always go according to plan.