The major connections between dogecoin and Shiba Inu are the fact that they are both memes coins
It is not their connection. You can not say Dogecoin has connection with many other meme tokens because they have names from many dogs.
Shiba Inu is presently up to almost 380% within the last few weeks and also saw dogecoin did a similar price hike in the previous month which have proven to the fact that both coins have been on a contesting mood in this altcoin season between Shiba Inu and dogecoin which is your most preferred choice for investment?
If you choose one from two meme coins: Dogecoin and Shiba Inu, the choice should go to Dogecoin.
Don't let your mind is blurred by promises from Shiba Inu. They have plans for NFT, smart contract, lock in DeFi pools, etc. and Dogecoin only has its use case as a payment method.
It will take Shiba Inu a few years to really become a competitor with Dogecoin, and take over the leadership of meme coin ecosystem. Dogecoin is safer as investment than Shiba Inu.