I think it is hard to give a general answer, what is best depends not only on what you consider best, but it may vary from conference to conference, and the audience.
But switching to an online conference is exactly what we did (The Perl & Raku conference). And although it's not an academic conference, many of the issues that were relevant to us, maybe relevant to you as well.
Our conference was scheduled for June, in Houston, Texas. We did both postpone and organize an online conference. Our conference is held yearly, in rotating cities in the USA (and sometimes Canada). We postponed the physical conference to 2021, to the same location. It did help that the hotel where the conference was being held was willing to work with us, and we could move the contract to the next year without much fuss. Groups who were working on bids for the 2021 conference were asked to work on a bid for 2022 instead.
We also decided to do an online conference. Partially because we had already accepted talks, and we wanted to give speakers an opportunity to present anyway, and partially because we felt that it takes way less resources to organize an online event than a physical event -- there is no venue to deal with, no catering, no travel arrangements for invited speakers, etc.
We did attract less submissions for the online conference than the physical one -- where we normally have 3 or 4 four parallel tracks during a 3 day conference, we now have 2 parallel tracks over 3 days. And that is even taking into account we got more submissions from European speakers than normally: were they are usually not willing to travel to the US, and go to our sister conference in Europe instead, there is no travel time for an online conference. Also, the European conference, scheduled for September, got cancelled as well, and will not do a separate online version. But there have been a number of speakers who signaled that they do not want to present online, and quite a number of people who submitted for the physical conference, did not do it for the online one.
A decision which needs to be taken is, what tool are you going to use to broadcast the presentations? Requirements for us were: the software should work on Linux, Mac, and Windows, with no costs for users; minimal costs for the organizers were acceptable. It should handle a large enough audience. It should be interactive, but moderated (that is, audience is normally muted, but can speak when allowed by the moderator). We decided to use Zoom, and stream on YouTube. Audience who wants to interact must use Zoom, no interaction will be possible on YouTube.
Another issue to deal with with an online conference is the schedule and time zones. With a physical conference, everyone is together and hence, in the same time zone. We will now dealing with people in the USA (from East to West), Europe, and an invited speaker located in Australia. Hence we start the conference at 11 AM Eastern Time, which is early, but, hopefully, not too early on the West Coast of the USA, with the last events ending at 5:30 PM Easter Time, which is past midnight for most of Europe. Hence, when I was scheduling the talks, I put European speakers in the morning as much as possible, and US and Canadian speakers later in the day. The Australian speaker is scheduled at the end of the day, which will be the next day for him. And unlike the physical events, we did not schedule any coffee/lunch/dinner breaks, audience members are scattered over too many time zones to make this work out.
Not everything can carry over. There will be no (obviously) no social events. And while we usually have a few days before/after the conference were (paid) classes are given, we have now restricted this to a single class. We have not worked out whether there will be any BOF (birds of a feather) meetings, and, if so, how we want to facilitate this.
For us, this is going to be an experiment. We do not know whether it's going to be a success, we can only decide that afterwards. And even if it's a success, that does not mean every other online event will be a success (and so it the opposite, if we fail, that does not imply other online conferences can't be a success).
This doesn't exactly answer your question ("Is it a good idea to change the conference to an online one or it is better to postpone the real conference until the end of this pandemic crisis?"), but I hope this answer will help you decide whether it's a good idea for you to change the conference to an online one or whether it's better to postpone your conference.