Help: Coins and their Blockchains

I’m getting more and more acquainted with crypto but I’m still new. I’ve been using Trust Wallet and Binance.US

My question is, is it good practice/a good idea to keep coins in their native blockchain form? What are the pros/cons?

In my case, I bought some Dogecoin through the DEX on TW and ended up with Dogecoin (BEP2). I tried to send a couple to my Binance wallet (just for testing it) and got an error about the address not being “right”. Some google searches and playing around in TW showed me that there can be multiple versions of a coin even if it has its own native blockchain. Thus, they’ll have different wallet addresses depending on their blockchain. I wish exchanges would make this MORE APPRARENT because these conversion fees add up. I eventually want all my Doge in one place, but I see they are in different forms.

Should I convert them back to the Dogecoin blockchain form or is BEP2 or BEP20 better?