I purchased a free-standing, composite soaking tub from Devon & Devon (D&D) (they have a clawfoot, but I chose a different style). Two advantages of composite over acrylic: it holds the heat, and scratches or stains can be easily "buffed out" with light sand paper. The D&D tub has a satin-like matte finish. I use Windex to clean it. D&D is pricey, but after trying out tubs for months, it was my favorite, and I was willing to wait several more months for delivery. Other brands I considered: Wetstyle (from Canada), Bain Ultra, Toto, Kohler, Duravit, Blu Bathworks, Mti, Hydrosystems, Axor, and T&L. Zucchetti and V&A tubs were tempting - but I didn't like the look of the exposed drain pipe.

I went with the lower quote in my last house to install a pedestal tub. It had a very slight leak and this guy eventually refunded my money and gave up trying to fix it. He said he thought it was because of slight movement when getting in/out of the tub was the cause. I ended up having it reinstalled by a very large plumbing company and it was 1K, they put some type of concrete like base under it to prevent any movement and they guaranteed the work. If your builder is going to do the work for 1K and guarantee it I would go with it. Less hassle and no issues if any warranty issues later. At the most you would save a few hundred, however you could be giving up a warranty and it would just not be worth it.

Or does the tub filler get secured onto a stringer installed between the floor joists?

I think it depends on how you live and if you're planning for resale. I am a bath person and chose an insert so that I could have an air jetted tub, have room for candles, bath salts, etc. and for ease of cleaning around it. I was told that it can sometimes be difficult to clean around free standing tubs, especially in a smaller space. Also, we wanted a larger one as my husband enjoys it after a long day of cycling. The tub insert may not be the rage right now but it functions best for us.