Usually neither first — you need your Google Business Profile sorted. A website with no traffic is a billboard in the desert. It can be beautiful and still send you exactly zero calls, because nobody is typing your company name into Google. They’re typing "plumber near me."
That search is answered by the map pack, and the map pack is driven by your Google Business Profile — not your website. So for most local and home service businesses the order that actually makes money is: get the profile right, get reviews coming in, then make the website earn its keep.
If your current site already loads fast, works on a phone, and clearly says what you do and where you do it, we would much rather spend your budget getting you found than rebuilding something that works. We’ll tell you which one you need on the free consultation — including when the honest answer is the cheaper one.