Power Rangers borrowing from Sentai
The most obvious would be changing the cast, suits, stories, themes, and series every year. Changing the suits wasn't done until Zeo, while changing the cast annually started with Lost Galaxy but wasn't completely decided on until after Lost Galaxy was done. The original cast of Lost Galaxy had a two year contract. Every since Lost Galaxy, the franchise has tried to make each season as stand alone as possible.
Another idea taken from Sentai was the annual team-up episodes with the previous year's team. This was first done in Power Rangers Zeo with the two part episode Rangers from Two Worlds when the Zeo rangers teamed up with the Alien rangers. This however, wasn't fully implemented until Lost Galaxy teamed up with In Space during the episodes To the Tenth Power and The Power of Pink. However, when Lost Galaxy came out, originally there were no planned team-ups with In Space. But when actress Valarie Varone (Kendrix/Lost Galaxy Pink) was diagnosed with Leukemia, she had to be replaced quickly. The plan was to have a team up with In Space, kill her character off, and have Cassie (Turbo/In Space Pink) replace her. After the team-up, Patricia Ja Lee filmed one additional episode but then left due to a contract dispute. Despite this, the production crew was still able to use the team-up, and eventually replaced Kendrix with Karone, the former villain Astronema. After lost Galaxy, annual team-ups became a yearly occurence.
Anniversary team-ups such as Forever Red and Once A Ranger were borrowed concepts respectively from Gaoranger vs. Super Sentai and Boukenger vs. Super Sentai respectively. While the plots in each episodes are completely original, the idea of having all red rangers team up, for example, was borrowed from Gaoranger vs SS. The same goes for Once A Ranger.
As mentioned in a previous post, Power Rangers RPM had a very Sentai-like cast with many characters being similar to previous Sentai characters. This includes Dillion being similar to Gai from Jetman, Summer being similar to Ran/Gekiyellow, and hyperactive comic relief power rangers such as Ziggy, Gem, and Gemma that while are pretty common in Sentai, are pretty rare in Power Rangers.
Sentai Borrowing from Power Rangers
Magiranger vs Dekaranger introduced the canon immigrant, literally. Sentai borrowed the red ranger battlizer from Power Rangers SPD to give Ban/DekaRed a new weapon from the Fire Squad that he was promoted to.
Head or floating head like characters such as Mr. Voice from Boukenger and Master Head from Goseiger are likely partly inspired by Zordon.
Jan/GekiRed seems to be inspired by Cole, from Power Rangers Wild Force. Both characters have essentially the same story. Both being red rangers, both being newbies to their teams after growing up in the jungle. Both had their parents killed by their series respective main villains (though the stories are slightly different). Both also tend to overact at times, and both characters were on beast-themed seasons.