In an attempt to answer this question more technically, let's try to define what we mean when we say abrupt change in temperature or high variability. I'll use airport stations for both cities, just to eliminate some flukiness due to UHI.
On a intra-day basis, that could mean diurnal range, i.e. whichever place has the largest average difference in temp throughout the day.
Well, Austin's annual average of 23.8 F (13.2 C) is quite a bit higher than Toronto's 17.5 F (9.7 C). But, maybe you don't care about average diurnal range and you only want to know which is capable of more extreme diurnal ranges.
If we take a look at the largest diurnal ranges per year from 1991 to 2020, we see that Austin's annual average largest diurnal range is 48.8 F (27.1 C) while Toronto's is only 37.2 F (20.7 C). So Austin is far more likely to have "extreme" diurnals.
But...maybe you mean abrupt change from one day to the next (daily variability). There are two ways to quantify this.
First, we can take the average of the difference from one day to the next. The "average difference in mean temp between consecutive days".
Austin's annual average is 4.0 F (2.2 C)
Toronto's is 4.7 F (2.6 C)
The other way is the find the largest difference in mean temp between consecutive days you can expect in an average year.
Austin's average annual largest difference is 22.9 F (12.7 C)
Toronto's is 21.6 F (12.0 C)
As shown by this data, Austin is more stable than Toronto on a day-to-day basis, but is slightly more prone to large swings in temp from one day to the next, occurring between these stable periods.
Conclusion: Austin sees more abrupt changes in temps within a single day, but they're almost tied when it comes to changes from one day to another.
