Having been in a similar situation (better hours, 40% pay increase, better/newer tech), if I was serious enough about working at the other company I would just turn in my notice and be done. For 10% or so I might give negotiating a try but, if the jobs are similar, a 50% gap (plus benefits) is massive and indicates the current company isn't all that interested in retaining employees by keeping them near market wages and I'd prefer to work elsewhere. I've known a few folks that were wooed by their existing employer to stay with matching salaries or better projects but it usually didn't work out well in the long run and they wound up leaving in a few years, anyway. Companies (like people) don't really change so if they have a habit of low pay or poor benefits today, they'll likely still have the same problem tomorrow.
In my case, my existing employer offered to match the pay but I still declined. My boss actually apologized for my low salary and said he understood why I left. I once got a 10% raise because my salary was too far below the minimum set by HR for my role - that was the day I stared looking. A funny thing in the interview process for the new job I provided my desired salary range and I based it on my current salary +20% or so and they came back with +40% on the first try. It was nice working for a boss that didn't play games and payed people what they were worth.
