There is an unconfirmed rumor that the Chora might reopen as a mosque in May. The problem is that the renovation/conversion was originally supposed to include covering all the mosaics, basically everything worth seeing at the Chora. There has been a lot of negotiation between UNESCO and the Turkish government for years, and I don't know what was finally decided.
I wouldn't make any plans to visit the Chora until you can confirm from reliable sources that the site is open and that the mosaics will be visible.
I would highly recommend visiting the Hagia Sophia, regardless of lines, entrances fees or restricted areas. I hate crowds and lines, but the Hagia Sophia is worth it. It is truly magnificent. The mosaics at the Chora were wonderful when I visited in 2015, but the Hagia Sophia is in a different league.