Editors top 3 Okonomiyaki choices:
Even though okonomiyaki originates in Osaka, this specific store started in Hiroshima and made its way to Osaka with their original Onomichiyaki 1000JPY. This okonomiyaki dish's core ingredients are gizzards and fried flattened dried squid and is made by using Hiroshima style (Hiroshimayaki). The main difference is that instead of mixing all the ingredients together, you cook them in layers and it will always have noodles in them (yakisoba or udon). You can find this shop about 5 minutes from Kita-shinchi station.
Source: onomichimurakami
The first Yukari Sonezaki opened in 1950 and has since grown into a chain with a number of stores across Osaka. Their no.1 okonomiyaki dish is the special mixed grill with pork, squid, shrimp and octopus for 1350JPY .Another unique okonomiyaki is their Osakajo,“Osaka Castle”, which is a 1kg okonomiyaki with shrimp, pork, squid, octopus, scallop and fried eggs meant for a group of 3-4 for 4,600JPY.
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You can check out other Osaka stores here
Located in an alley full of restaurants called Hozenji Yokocho is Yakizen. They use their own recipes and sauce to make delicious okonomiyaki and one of their most popular ones is the Meibutsu Modanyaki with pork, squid, and soba for 1,330JPY. Modanyaki is another sub-style of okonomiyaki. Similar to Hiroshimayaki, it will always have soba in it but it is made in the Osaka way of mixing all the ingredients together. 
Source: yakizen
Editors top 3 Takoyaki choices:
About only 1 minute walk from Kintetsu Nippombashi Station (exit 7) is Takoyaki Ebisu. A small shop that sells delicious takoyaki at very attractive prices. You can choose between the following sizes; 8 pieces for 450JPY, 12 for 550JPY, 16 for 650JPY and you get to choose between a few different sauces like soy sauce or ponzu, at no extra cost. You can also add toppings like green onions 100JPY, garlic 200JPY and cheese 300JPY.
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If you happen to visit Tennoji park or Osaka Tennoji Zoo, and are looking for good takoyaki, we recommend visiting Ajinodaimaru. Only a few minutes from the zoo, and hard to miss with a giant red octopus sign above the entrance, Ajinodaimaru offers a large variety of dishes and among them are sets of 6 pieces of takoyaki will all kind of sauces like their secret sauce 330JPY, mayonnaise and cheese 385JPY. More than that, if you book more than two days ahead of time you can choose 3 ingredients and make your own takoyaki.
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Takoyaki Creo-ru specialize in making crispy takoyaki on the outside and soft inside. Like every restaurant, they keep their recipe a secret but they did reveal that the dough is made from using 7 different types of flour. You can order 6 takoyakis with a sauce of your choice out of 4 options for 430JPY, green onion topping is an extra 100JPY. We recommend trying one of their Gourmet series Takoyaki like the soft-boiled egg and green onions for 580JPY. 
Source: creo-ru