I do not agree with Jb1176 about deeper sinks being an "installation nightmare". I have a 9" deep single-bowl rectangular sink with offset drain and a large Waste King batch feed disposal (batch feed disposals tend to be larger than continuous feed disposals). There was no problem whatsoever installing it, nor in its daily use. As JB said, you need to check that your plumbing outlet will be lower than the outlet on the disposal for drainage. You don't have to pay a plumber to check this - just look online at the specs of the disposal you want, and also make sure you include the thickness of your countertop when adding it to the height from the top of the disposal to the disposal's outlet. Also, Insinkerator makes a compact disposal for those who do not have a lot of room under their sinks. As to your two choices of sinks in your posting, I do not have either one, but I have read quite often on this forum of people undermounting sinks like that Blanco Diamond 511-653. Furthermore, the Blanco website says specifically for that model, "ideal for both drop-in and undermount installations". The two sinks seem to need different size cabinet bases (33" and 36"), so make sure you have included that factor in your decision. Both sinks have the offset drain feature you like, although the Precis drain is offset in the rear center, but that still means you can set pans down in the sink without covering the drain since it is offset. Another consideration would be that, aesthetically, the Precis model is very contemporary, while the Diamond 511-653 could go in either a contemporary or traditional kitchen. BTW, you linked the 511-653 at Home Depot where it costs $476, not including sales tax. At Homeclick.com, where you've linked the Precis sink, that 511-653 is selling much lower, for $308, free shipping. I've linked it below. Here is a link that might be useful: Blanco Diamond 511-653 at Homeclick.com

Vigo farmhouse sinks are a Matte Stone which obviously means it has a soft finish on it. It absorbs EVERYTHING. I washed my hands and some of the dirt splashed on the walls. Had to scrub for a while just to clean that off. If you ever tough the outside with slightly dirty hands or anything else it will mark up like crazy. I returned my Vigo sink immediately. Just not worth the constant effort to me.

I have that one. I just measured. The center of the drain is 4.75 inches from the inside back wall of the sink.

This is one of these individual-preferences things. I personally find the Cascade confining, and would not have one for my kitchen. I like a big single bowl. I don’t care about having a shelf for draining or a shelf in my sink at all. That’s me, and others feel differently, while others feel like me. My advice is to go to a place that has the Cascade on display. Bring with you your most frequently-used pot or pan. Pretend to handle it in the display sink. Also do same with a single-bowl sink. See how you feel. You can’t go by internet photos and specs. You need to see one IRL. Edited you add: just noticed that @Lisa Versaci is responding to a 2-year-old post. Wish I’d noticed that before I took the time to respond under the impression the OP was still shopping for a sink. Sigh.