I had a look at the Samsung S10e and was so impressed I pre-ordered it after having already pre-ordered the largest Samsung 10s Plus. I still can't decide which pre-order I'm going to keep.
The S10e has a gorgeous display and great cameras, especially compared to the 5s. It's easier to find accessories for it than less popular brands like Sony. You will also get excellent stereo sound and you also still get the headphone jack, which is nice for anyone who has a good supply of wired earbuds built up over the years.
Battery life is said to be very good.
There is also the Google Pixel 3 and the upcoming Pixel 3 Lite to look at. You lose the headphone jack with the Pixel 3. I forget what the feature set of the Pixel 3 Lite is supposed to be.
I find Samsung devices to be more consistent in quality control this year vs Pixel. But Google customer service seems to be more accessible if you have a problem, assuming you're in the US. I'm on the mobile version of the site and cant see everyone's locations.
I'd personally go with the S10e because it does have the latest processors and best specs available and you can expand storage with a micro SD card, which have come down in price.
As someone who has an iPhone SE and an iPhone Xr, 8 Plus, Pixel 3XL, I'd say it will take some getting used to going from the SE to the S10e, but the S10e feels very comfortable sizewise compared to all the phones I've listed. But you gain a comfortable sized display.