There is a caveat to mention: keep in mind that compensation at these firms exhibits survivorship bias. A new grad engineer at Jane Street will receive around $300 - 400k all in first year compensation: around $150k base, $150k guaranteed end year bonus and $100k sign on bonus. From there, what typically happens is further recalibration a year later. Either you're good enough to maintain at least that level of comp, and you stay, or you're out within a year or two.
This means that you may not get an initial pay raise by joining, if you're extended an offer. Engineering offers from top trading firms are often an initial paycut, or an equivalent package, for anyone who is senior or higher at a place like Google and Facebook. You don't generally get to really significant compensation beyond tech until you're a few years in, and implicit in that assumption is that you'll actually stay there.
So let's say you're a new grad with offers from Jane Street, Citadel, Google and Facebook. You'll probably get $400k from Jane Street and Citadel and $200k from Google and Facebook, including sign on bonuses. If you join one of the trading firms right out of school, you'll develop an affinity for the work faster (if you're good enough to stay), and you can reasonably expect to make up to $1M/year by the time you're 30.
But now let's say you're L6/E6 at Google/Facebook. Maybe you're 30 and have $500k total compensation per year. Jane Street isn't going to offer you significantly more than half a million a year just because of your level in tech, unless they have a really pressing need and you're an industry expert. You will probably receive about the same package, with the possibility of making significantly more after developing more experience with their tech stack and work, after a year or two.
The "shock and awe" competitive packages are given to new grads who can be developed from day one, but senior hires require further calibration. There is a ceiling on what trading firms are willing to offer people who have exceptional promise but otherwise no domain experience in finance.
In any case the people I know at Jane Street are consistently exceptional. I highly recommend the firm if you're interested in their work. Likewise Hudson River Trading has a very similar profile but is smaller and has more of a startup feel to it.