Definition: Flexible wedge - > A wedge normally coated totally with special grade elastomer, usually rubber types NBR or EPDM based. Solid wedge: metal wedge with metal to metal seating. There are some hundreds (thousends?) of types and variations, but on a general basis (European):
Soft sealing gate valves (flexible wedge gate valves) main group from DN40(mm) up to most commonly used 250mm to 300mm (6-8inches) but readily avilable up to at least 1200mm. Pressure classes: low (PN 10 and PN16 (bars), mostly PN6 or PN10 above 8 inches but commercially available up to PN16 (All these classes below ANSI 150)
This group is most commonly used for drinking water and sewage water, and will seal thight with relatively long lifetime and low maintenance requirements, and have a low price, often lowest for any valve in range up to DN250. They are also allowed and used for natural gas (household gas) distribution, air conditioning, pressurized air, and other types of water distribution and neutral fluids. Usually housing (used as seating) is inside epoxy coated or (more limited) emailled.
Below these sizes rubber coated wedges are not practical or economical to produce.
For higher pressure classes or other media the rubber coating will/could give problems (gas bubble expansion within coating, not be compatible to temperature or fluids etc), and are of this reason not easily commercial available or selected produced.
The large group of metal seated gate valves have the minus that the sealing surfaces are more exposed to encrustations, corrosion, abrasion or cavitation (by not properly closed valves)than soft sealing gate valves.
If a soft sealing and a metal to metal sealing gate valve both hit the requirements of your application the soft sealing would normally be the cheapest, more mass-produced item. Be however aware of flow speed limitations, which is commonly lower for the soft sealing gate valve.
Also: depending on your chemical and total application requirements, other type of valves than gate valves could be considered, again also depending mainly on pressure class and size.