If you want a really good book on WW2 British escort design, "Atlantic Escorts" by D. K. Brown is probably the best thing in print.
Basically we had to do what we could with the shipyards available - an oversimplification, but they essentially fell into three categories as far as building escorts were concerned.
1. Those capable of producing small commercial ships - they got to build the Flowers and then the Castles. The Castle was a quantum leap on the Flower in AS armament, but not much else.
2. Those capable of producing slightly larger commercial ships - they got to build Rivers (some of which were built in the US for the RN as the Colony class), Lochs and Bays. The Loch was essentially a follow on River with a vastly better AS sensor and weapon suite - the best in any navy in WW2. Toward the end of the war something like 60% of double squid salvoes killed a u-boat. Bays were Lochs optimised for anti aircraft warfare in the light of the Japanese de-emphasising subs and emphasising aircraft.
3. Shipyards that could build to naval standards - these built sloops such as the Black Swan class, but not many of them as it made sense for them to focus on the construction of other warships - sloops were not really good value compared to the corvettes and frigates and were not much cheaper than a destroyer to build.
Remember also that, whilst some Flowers and Rivers went to the USN to stem their escort crisis, we then took on lots of US DEs as the Captain class. The US DEs were built in truly epic numbers and scrapped just as fast post war when it was felt that fast battery subs made them obsolete.
Evaluating the effectiveness of individual classes vs each other is tricky as the faster escorts, including converted V&W destroyers, would be the ones dispatched from the convoy to prosecute targets whereas the corvettes, because of their low speed, would remain in the screen.