This is just a summary and I'm aware that there are more in-depth threads here on EF for some of the ideas below.
SWITZERLAND
Some things are cheaper here. Electronics are often priced identically world-wide and hence vary only on local taxes. Swiss VAT is 8% so most electronics are cheaper here.
Fruit & veg in the supermarkets are often not much more than abroad, but they tend to go off very quickly due to the poor supply chain most of them have. Manor have regular discounts on things, and the quality is good. Coop often 50% off things towards the end of the day, but fruit/veg/salad stuff really has to be eaten that day.
Asian food (the place by SBB and NAM near Wettsteinplatz) is cheaper than in France and Germany for almost everything, which is a bit of a surprise. Probably due to import taxes as we're outside the EU.
GERMANY
Germany is the cheapest place to shop (out of Germany, Switzerland and France) for almost everything. Cleaning products are often 1/3 the Swiss prices and noticeably cheaper than France. Almost any branded food product is cheaper in Germany,
Marktkauf - just over the Weil am Rhein border. Tram 8 goes there. It's owned by Edeka, which is an up-market supermarket chain, so the Edeka own brands are good quality. The shopping experience is anything but, however. Don't go at peak times (especially with a car) and you'll be fine.
Rewe - there's one in Lorrach (where Migros was) and also in Weil am Rhein, where the Tram 8 will now take you. It's a bit cheaper than Marktkauf but has less stock. I usually just go to Marktkauf.
Hieber - it's a more upmarket shopping experience and the deli counter is good. There's one in Lorrach and another in Grenzach. If you insist on buying fish in Germany this is where to get it. Prices are not actually much more than Marktkauf, if at all.
FRANCE
France is more expensive than Germany for most things but as the southern Germans, like the Swiss, don't seem to care for fish or a variety of cakes/bread, France is where to go for these. Plus the deli counters are excellent.
Geant Casino - This is about 5-10 mins walk from the centre (crossroads) of St Louis. The Distri bus goes there from Schifflaende. It's convenient if you're cycling, but despite recent renovations is still far behind E.Leclerc.
E.Leclerc - this is just past St Louis in a small shopping complex behind McDonalds. The Distri bus goes there too, making it a no-brainer to go here instead of Casino. The fish counter and bakery are excellent, and it's cheaper than G Casino. Good and fresh selection of fruit and veggies; better than Marktkauf and Rewe, and more choice (albeit not as posh as) Hieber. I usually grab my fish and cakes from here, hit the deli, then cycle to Marktkauf for the rest.
Carrefour - this is on the edge of Mulhouse. It's a proper hypermarket so bigger than any of the others mentioned above, but that's more due to its non-food section. The food section is no better than E.Leclerc so not really worth the trip, although Mulhouse itself is actually not a bad destination with some good restaurants. If you're into cycling, it's a lovely 35km from Basel almost entirely off road and along the canal from Huningue. I went today and cycled back, but you can take the train back for around 12€ (bikes on trains are free).
TAXES
In France you need to spend over 150€ to get the VAT back, and many shops won't bother doing it anyway although the supermarkets above will. I've never done it, so be prepared for the usual French efficiency at customer service ...
In Germany they seem to love giving the tax back. It's 19% on non-food stuff (making cleaning products even cheaper!) and 7% on food/drink. Almost every shop near the border will give the right forms; you need to get it stamped as you export the goods (ie at the German/Swiss border by the Germans) and then take it back to the shop another day (officially) who will give you the 19% back. Each shop seems to have a different procedure and I can't be arsed explaining it all. Except to say .. Karstadt (dept. store in Lorrach) give forms which say you need to use something like Global Blue (which take half the tax as commission). Ignore it and take it, stamped, back to the shop. You get the full 19% back.
Of course, there are import limits into Switzerland. They're all documented clearly here: http://www.ezv.admin.ch/zollinfo_pri...x.html?lang=en
I've not proof-read the above, but it should make sense.