Having someone else paying you rent is always going to be the better deal financially. The question is, what does $450k buy in the neighborhood in which you want to live, vs $800k?
I'm going to assume you can afford either option (buying a $450k home and not selling, or an $800k home and selling your current one) whether someone's paying you rent or not.
Let's make up some numbers here; a $450k home, financed 80/20 (360k principal) at 4% for 30 years will cost you about $1720 in P&I payments per year (plus escrows such as RE taxes, PMI, and homeowners insurance where applicable).
An $800k home financed 80/20 (640k principal) at 4% for 30yr will give you payments of about $3,055/mo before taxes and insurance.
So, the worst case overall is that you buy a 450k home in the new neighborhood and are not, at any given time, collecting rent on the old property. That would (assuming the mortgage terms on both home loans were comparable) cost you $3440/mo and you'd be living in a $450k home in a neighborhood where 450k may not buy a home as nice as the one you moved out of.
The question as I stated above is this; assuming you had a reliable tenant in your home for the entire remaining life of the loan on your current home, which is more acceptable to you: buying $450k of home (which might be a downgrade in sqft or amenities) and paying $2020 in P&I, or paying about a grand more ($3055/mo) for a much nicer home in the new location?
Strictly from a money perspective, the renter is going to be the best option, IF you get reliable tenancy for the entire life of the mortgage on that house; you'll be paying $2020/mo for 30 years, which is $727,200, to end up with $950k of total home value (plus adjustments for actual home value appreciation/depreciation). That's the only way you'll come out ahead on any mortgage; have someone else pay most of it for you. If you don't rent, the $800k home will cost you $1,099,800, while two $450k homes will cost you $1,454,400. The percentage of home value over total payments for the 800k home would be 72% (you will have paid 137% of the value of the home), while you will have paid 153% of the value of two 450k homes.