Question about DLC not downloading because I don't have enough memory on my console

No. It's not possible to download anything directly from the website. You can use a flash drive as extra storage space on the console and use that.

Hey there!

Unfortunately the DLC won't transfer, as The Handsome Collection is technically a separate/different game from the initial 360 version.

Right, that part I understand! I guess my question was not clear enough, sorry about that.

My question was about downloading BL1 GOTY dlc content on XB1, even though I already downloaded it on my 360.

Hey guys, sorry to hear about the issue playing GoW! To be sure, have you tried deleting the DLC from memory,
clearing the cache, and then re-downloading the DLC? Please let me know if you have questions about any of these steps!

You aren't going to like at least one of my two solutions:

1) delete and then from your download history re-download the DLC. It is possible that the game is hanging because you HAD the DLC, and now that you don't, the game is confused.

2) this one slightly builds on the first - It is possible that your game is "set" to have the DLC. Because you don't have it (having deleted it), it doesn't mesh with some bit of code that for those without the DLC (like myself) lets them play seamlessly.
So if #1 doesn't work, you're going to have to delete the entire game file on your console (or memory stick, where ever it saves to) and start all over again.

Those are what I think would fix the issue, but no promises.

They should have made sure they were making the right decision when purchasing the 4GB console. It's cheaper but not enough memory because your going to have titles updates, dlc items , game saves, and some reserve space taken away by the system.